Ebook kỹ thuật số lý thuyết và ứng dụng phần 1

Cac mach digital dude dira vao sirdung trong hang loat cac san pham dien tif, nhi/ cac thiet bi vien thong, may ti'nh, ti_r dong hoa, cac do choi co mach dien tCr, cac he thong nghe nhin

LQ1 H 0 3 B & I

Ngay nay, ky thuat digital dUOc ap dung rong rai trong nhieu ITnh virc Cac mach digital dude dira vao sirdung trong hang loat cac san pham dien tif, nhi/ cac thiet bi vien thong, may ti'nh, ti_r dong hoa, cac do choi co mach dien tCr, cac he thong nghe nhin, do gia dung, dung cu do luting, dung cu y te va quan sir, cac tur dien dien tCr_

Sach Ky thuat digital - ly thuyet va Crng dung gidi thieu nhCrng kien thud co ban ve ky thuat digital va mot so irng dung trong doi song Be tiep thu cac kien thud de cap trong cuon sach nay, ban doc can co nhCrng kien thud pho thong ve toan va ve mach dien tir Ky thuat digital dude nghien ciru trutic hoac nghien cuti song song v6i mon hoc dien tir co ban vi cac kien thud ve linh kien ti'ch cifc rdi rac khong phai la dieu kien doi hoi trutic het

Co the noi, cuon sach nay la ngirdi ban dong hanh cua cac ban ham thich dien ti!r digital, cua cac cong nhan nganh dien tu” - vien thong va may ti'nh cGng nhif cua cac cong nhan lanh nghe thuoc cac ITnh vu t co lien quan den cac mach dien

tu1 digital Cuon sach nay dirpc xem nhir la tai lieu tham khao hCru dung vi ti'nh th u t dung va de hieu cua no doi vdi cac sinh vien cao dang va dai hoc nganh dien tCr - vien thong va may ti'nh

Sach Ky thuat digital - ly thuyet va u"ng dung co 11 chirong Chi/ong 1 khai quat ve cac he thong so nhi phan, bat phan va thap luc phan, moi lien quan giCra cac he thong nay vdi he thong so thap phan, chi/Ong nay cGng gidi thieu tong quan cac ma diroc sCr dung trong ITnh vi/c vien thong va may tfnh Chutfng 2 gidi thieu ve dai so logic, phan tich va tong hop mach logic, cac djnh ly De Morgan, cac phifOng phap toi gian mach bang bang Karnaugh, bang cac dinh ly va dinh luat cua dai so logic Chi/dng 3 gidi thieu cac mach xir ly so lieu, de cap den cac bo ghep kenh, phan kenh, cac bo giai ma, ma hoa, bo tao va kiem tra bit chan le Noi dung Chi/ong 4 noi ve phep cong, phep trif so hoc, cac phep bu 1, bu 2 va cac bo niTa cong va cong day du, de tirdo, ta hieu di/Oc can ke cac bo cong va bo trir ChiTOng

5 gidi thieu cac ho IC TTL va CMOS, noi dung de cap trong phan nay giup ta co cac kien th u t co ban de sCr dung co hieu qua va phoi ket hop di/oc cac ho IC TTL

va CMOS trong cac mach digital Noi dung cac Chuting 6, ChiTOng 7 va ChGOng 8 di/oc u'ng dung nhieu trong cac mach dien tu1 digital thong thuting ChifOng 6 gidi thieu cac loai flip flop RS, RS dong bo tTnh, flip flop D, flip flop JK va flip flop JK Master-Slave; ngoai ra, con gidi thieu trigo Schmitt, loai trigo co dac ti'nh quan trong, dude su' dung de tao nen cac xung nhip; Chudng nay cung gidi thieu cac loai mach dao dong, mach tao xung nhip Noi dung ChUdng 7 thirc chat la cac u’ng

3

dung dac ti'nh cua cac flip flop diroc ti'ch hap trong cac IC de thirc hien cac phep di chuyen so lieu Trong chirong 8, noi dung diroc de cap la cac loai bo dem va cac Mod dem; tir chirong nay, ta thay diroc cac cau true va cac iru nhiroc diem cua cac loai bo dem Chirong 9, bo nho ban dan va chirong 10, chuyen doi A/D va chuyen doi D/A, hai chirong nay gidi thieu ve nhCrng nguyen ly cau tao co ban va cac dac ti'nh cua cac bo nho ban dan, cac bo chuyen doi A/D va chuyen doi D/A, giup ta co the Crng dung cac bo kien nay trong cac mach dien tir digital Chirong 11 dira ra mot so mach Crng dung ky thuat digital, nhir trong dung cu dem tan, do do rong xung va trong dong ho digital Co the xem chirong 11 nhir la mot so bai tap Ion, Crng dung ky thuat digital, tir do, ta co the van dung ky thuat digital vao cac Crng dung khac trong doi song hang ngay.

Voi dung y cuon sach Ky thuat digital - ly thuyet va Crng dung diroc viet de pho cap rong rai kien thCrc ve digital, voi cach trinh bay de hieu, co nhieu vi du, nhieu bai tap va loi giai Tac gia rat mong cuon sach diroc dong dao cac cong nhan lanh nghe cung nhir cac sinh vien cao d in g va dai hoc nganh dien tir - vien thong va may ti'nh, cac ban yeu thi'ch ky thuat dien tir digital rut ra diroc nhCrng dieu

bo ich tu” cuon sach nay

Trong qua trinh bien soan va in an, cuon sach khong the tranh khoi con nhCrng thieu sot Chung toi rat mong ban doc thong cam va gop y xay diing, de trong Ian tai ban, cuon sach diroc hoan thien hon

Chung toi xin gCri toi Ban Bien tap Nha Xuat ban Lao dong - Xa hoi loi cam on chan thanh ve sir giup do qui bau cua Qui Ban, de cuon sach s6m dGOc ra m§t ban doc

DO KIM BANG

CHUONG 1

HE THONG SO V A M A■

Hoc xong chuang nay, hoc vien co kha nang:

□ Hieu dwoc cac he dem thap phan, nhi phan,

bat phan va thap luc phan.

□ Chuyen doi d'uoc cac so tit he thap phan

sang cac he nhi phan, bat phan va thap luc phan

va ngwoc lai.

□ Tinh d'L/oc cac gia tri cua cac so phan

nguyen va phan phan tit cac he nhi phan, bat phan va thap luc phan sang cac so tuong ditong cua he thap phan va ngitdc lai.

□ Hieu diroc cac cau true mot so ma thong

thudng dung trong ky thuat digital.

TONG QUAN

Khi noi den so dem, moi ngirdi deu nghT ngay den he thap phan v6i 10 con so: 0, 1,2, 3, 4, 5, 6, 7, 8, 9 May vi tinh hien dai khong xir ly so thap phan Thay vao do la he thong so nhi phan sir dung 2 con so: 1 va 0 Nhi/ng khi sir dung so nhi phan, muon the hien mot so thap phan co tri so tirong doi Ion bang so nhi phan thi so nhi phan do kha dai Do do, ngirdi ta thirdng sir dung cac so bat phan va thap luc phan de rut ngan chuoi so nhi phan

Chirong nay trinh bay cac he nhi phan, bat phan va thap luc phan v6i muc di'ch khong chi dem diroc cac so theo cac he dem tren day ma con nghien ciru each chuyen doi tir he dem thap phan sang cac he dem nhi phan, bat phan va thap luc phan va ngiroc lai Chu’Ong nay cung de cap den cac ma nhi phan thirdng diroc su' dung trong cac he thong digital

5

1.1 SO NHj PHAN

Cac may vi ti'nh va cac he thong digital deu dira tren co so hoat dong nhi

phan (2 trang thai) Vi du, khoa chuyen mach trong Hinh 1.1a co the diroc dong lai

hoac mo ra Do do, khoa chuyen mach la mot vi du ve thiet bi nhi phan don gian nhat

Tranzito trong cac mach dien tir dung trong cac he thong va cac may tinh digital diroc thiet ke de hoat dong tirong hop v6i he thong nhi phan, do la hien tirong ngirng dan hoac dan bao hoa cua tranzito Ket qua la 6 ngo ra cua mach tranzito co mot trong hai trang thai mire dien ap cao hoac mire dien ap thap Khi quan sat tin hieu digital tren may hien song thay dien ap hoac 6 m u t thap hoac 6 mire cao Cac tin hieu digital nay thay doi mire dien ap khi may vi ti'nh hoat dong,

cac dien ap nay xuat hien nhir la cac xung (Hinh1.1b)

Hinh 1.1 Cac vi du ve sir dung so nhi phan

Tom lai, cac khoa chuyen mach, cac tranzito va cac linh kien digital khac deu dira tren co so he nhi phan Oieu do noi len rang so nhi phan rat thuan tien khi dung vao viec phan tich va tong hop cac mach digital Ngoai ra, can biet cach dem

so nhi phan va chuyen doi so nhi phan ra thap phan va ngiroc lai

1.2 CHUYEN DOI NHI PHAN - THAP PHAN

Co the bieu dien so nguyen bat ky thanh cac so don vi, chuc, tram, nghin

Vi du, so thap phan 2945 co the viet thanh:

2945 = 2000 + 900 + 40 + 5( 1 1 )

Bieu dien diroi dang luy thira cua co so 10, bieu thirc (1.1) co the viet lai la:

2945 = 2.103 + 9 102 + 4 101 + 5 10°

Vi tri cac con so

Moi vi tri con so trong day so 2945 co mot trong so va he so.

Cac luy thi/a co so 10 :103, 102, 101, 10° la cac trong so.

Cac so 2, 9, 4 va 5 la cac he so

Ti'ch trong so va he so cho gia tri cua moi vi tri con so

Tong tat ca cac ti'ch cho gia tri cua so thap phan do

6 vi du tren, 2 nhan vdi trong so 1000, 9 nhan v6i trong so 100, 4 nhan vdi trong so 1, tong so la:

Bieu thirc (1.3) viet dirdi dang thap phan:

Noi cach khac, moi vi tri so cua so nhi phan co mot trong so Vi tri thCr nhat 6 ben trai, so 1, (trong so nhoi nhat Vi tri thCr hai tir ben phai co trong so 2, so ben trai lien ben co trong so 4

Cac trong so nay co so mu cua luy thira 2 tang len, do do, co the viet phirong trinh (1.4) nhir sau:

7 = 1 22 + 1 21 + 1 2°

Moi khi gap so nhi phan ta co the xac dinh diroc mot so thap phan tirong dirong nhir sau:

1 Khi co so 1 6 mot vi tri con so, hay cong trong so cua vi tri do

2 Khi co so 0 6 mot vi tri con so, bo qua trong so cua vi tri do

Vi du, so nhi phan 101 tirong dirong vdi so thap phan la:

4 + 0 + 1 = 5Mot vi du khac, so nhi phan 1011 tirong dirong voi so thap phan la:

8 + 0 + 2 + 1 = 1 1

Phi/dng phap doi so nhj phan ra thap phan theo thu tuc sau:

1 Viet so nhi phan

2 Viet tri/c tiep dirdi so nhi phan cac so 1, 2, 4, 8, 16 va viet tu1 phai qua trai

3 Neu co so 0 0 mot vi tri con so, xoa bo trong so 0 vi tri do

4 Cong cac trong so con lai ta diroc so thap phan tirong dirong

Vi du: Hay chuyen doi so nhi phan 101 thanh so thap phan tirong dirong:

- Phan phan cua so nhj phan

Ta da nghien ciTu phan nguyen Vay phan phan cua so nhi phan diroc chuyen doi thanh so thap phan tirong dirong nhir the nao?

Vi du, so thap phan nao tirong dirong vdi so nhi phan 0, 101? Trong trirdng hop nay cac trong so cua cac vi tri tir phia phai dau phay cua so nhi phan la: 1/2; 1/4, 1/8, 1/16 v.v

Neu viet diroi dang luy thira cua 2, cac trong so la:

- So nhj phan hon hop

Doi vdi cac so hon ho'p (cac so co ca phan nguyen Ian phan phan) ta thirc hien cac quy t§c chuyen doi da thao luan 6 tren cho cac phan nguyen va phan phan Cac trong so cua cac so hon hop la:

v V 23 22 2 1 2°, 2~1 2 "2 2“3

/

dau phay nhi phan

- Bieu do may vi tinh

Khi nghien cifu cac so nhi phan, ta hieu biet sau sac them ve cau tao ben

trong cua mot may vi tinh Hinh 1.2 la cac phan co ban cua mot may vi ti'nh diroc

gidi thieu nhir sau:

Ngo vao: la noi dira chirong trinh va so lieu vao may, 6 may vi tinh ngo vao bao gom ban phim de chuyen doi ky tir (chCr va so) thanh chuoi cac so lieu nhi phan

Bo nhd: la noi chirong trinh va so lieu diroc liru trir trudc khi tinh toan Cung

vay, khi ti'nh toan, bo nhd liru tru” cac tra loi trung gian, tirong ti/ nhir cach ta v ln lam khi ti'nh toan Bo nhd cua may vi tinh gom co ROM (bo nhd chi doc) va RAM (bo nhd viet va doc)

Dieu khien: phan nay cua may vi ti'nh trong qua trinh ti'nh toan khong nhd con

ngirdi can thiep vao Phan dieu khien noi cho cac phan cua may vi ti'nh cach xir ly

so lieu nhir the nao ^

Phep tinh so hoc va logic: phan nay la cong, trCr, nhan va chia Phan nay

cGng thirc hien cac phep tinh logic nhir OR, AND, NOR, NAND v.v

Ngo ra: la phan de chuyen Idi giai cuoi cung ra ben ngoai Phan ngo ra cua

may vi ti'nh la man hinh cho phep ngirdi sir dung thay diroc cac so lieu da diroc xiriy-

Trong bang dirdi day thong ke cac luy thira cua 2 va so thap phan tirong dirong cua chung, cung cac so K Ky hieu K thay cho 1024 Do do, 1K b ln g 1024 2K bang 2048 4K b ln g 4096 v.v Nhieu may vi tinh ca nhan (PC) co cac bo nho 64K, dieu do co nghla la chung co the liru trir 65.536 byte trong phan bo nhd chi

ra 6 Hinh 1.2

Bang 1.1 Cac luy thira cua 2

CAC LUY THUA CUA 2

SO THAP PHAN TUUNG OUtfNG

CAC LUY THUTA CUA 2

SO THAP PHAN TUtfNG BlTCfNG

1.3 CHUYEN DOI THAP PHAN - NHj PHAN

Cach chuyen doi so thap phan thanh so nhi phan tirong dirong la cach tien hanh ngiroc vdi cach chuyen doi da di/oc mo ta 0 tren

+ Vi du, muon chuyen doi so thap phan 9 thanh so nhi phan tirong dirong, dieu can thirc hien la bieu thi diroc 9 la tong cua cac luy thira cua 2, roi viet 1 va 0

0 cac vi tri cua cac con so:

- Phirong phap chia tuan tir cho 2

Phirong phap pho bien de chuyen doi cac so thap phan sang nhi phan la cach chia tuan tir so thap phan cho 2 viet so du” sau moi phep chia Cac so dir du'o'c slip xep theo thir tu ngu'dc se cho ta so nhi phan tuong dirong Cach tot nhat

de hieu phirong phap nay la thirc hien vi du dudi day:

Cach chuyen doi so thap phan 53 ra so nhi phan nhir the nao?

Thi/c hien chia

'<&

JZO

So co trong so Idn nhat (MSD)

- Phircfng phap trir

Be thirc hien viec chuyen doi so thap phan sang so nhi phan, ngoai phirong phap chia lien tiep so thap phan cho 2, con co phirong phap trir bang cach don gian viet cac gia tri cua cac so luy thira 2 cho den so co gia tri gan vdi so thap phan can chuyen doi Sau do, trir lien tiep so thap phan cho cac so luy thira 2 Neu phep trir di/oc thirc hien vi so luy thira nho hon so thap phan, ta viet so nhi phan 1 vao vi tri bit tirong Crng v6i so luy thira 2 Neu so luy thira I6n hon so thap phan 6 phan dir, ta viet so 0 vao vi tri tirong ting cua so luy thira do va tiep tuc thirc hien cac bu6c cho cac so luy thira 2 ke ben Oe biet cach chuyen doi so thap phan sang so nhi phan bang cach trir, tot hon het ta lam vi du sau day

Vi du, hay chuyen doi so thap phan 50 sang so nhi phan So luy thira 2 Idn nhat nho hon so 50 la 32 Viet cac so luy thira 2 tir 25 tro xuong Phirong phap trCr diroc thirc hien nhir sau:

Ta nhan phan phan cua so thap phan voi 2, ghi lai so nhd 6 vi tri nguyen Cac

so nho doc theo chieu xuong la phan phan cua so nhi phan

1 1

Vi du: Chuyen doi so 0,95 ra so nhi phan nhir sau:

Ket qua la: 0,9510 = 0,11110012

- Doi so nhj phan gom toan so 1

Khi nao mot so nhi phan co toan so 1, co the tim so thap phan tirong dirong bang cach dung cong thu’c sau: so thap phan = 2n - 1, 6 day n la so bit

+ Vi du: 1111 co 4 bit, do do, so thap phan tirong dirong la:

So thap phan 24 - 1 = 15

Ket qua la: 11112 = 1510

+ Mot vi du khac: 1111 1111 co 8 bit, nen:

So thap phan tirong dirong = 28 - 1 = 255

Ket qua la: 1 111 1 11 12 = 25510

Co so cua mot he thong so bang so cac con so ma he thong do sir dung

He thong so thap phan co co so la 10 vi he thong nay co cac con so tir 0 den

9 He nhi phan co co so 2 vi no chi dung so 0 va so 1 He bat phan co co so 8 Ta

co the sir dung 8 con so thong thirdng, do la 8 con so dau tien:

0, 1, 2, 3, 4, 5, 6, 7

(khong co con so 8 va 9 trong he thong so bat phan)

Cac con so trong he bat phan co cung y nghTa vat ly nhir cac so thap phan

- Sir chuyen doi bat phan - thap phan

Sir chuyen doi tir bat phan sang thap phan nhir the nao? Trong he bat phan moi vi tri con so tirong ung voi luy thtia co so 8 nhir sau:

83 82 8 1 8° , 8“ 1 8‘‘2 8~3

dau phay bat phan

Do do, de chuyen tu" bat phan sang thap phan, ta nhan moi so bat phan vdi trong so cua no va cong tat ca cac ti'ch iai:

Vi du: so bat phan 23 chuyen doi sang thap phan nhir sau:

2 x (81) + 3 x (8°) = 16 + 3 = 19Mot vi du khac, doi so bat phan 257 thanh thap phan:

2 x (82) + 5 x (81) + 7 x (8°) = 128 + 40 + 7 = 175

- Chuyen doi thap phan sang bat phan

Sir chuyen doi thap phan - bat phan diroc thirc hien nhir the nao?

6 day, thay the cho phep chia cho 2, ta chia cho 8 (co so 8), ghi lai phan dir sau moi phep chia Cac so dir theo mot trat tir ngiroc tao nen so bat phan

Vi du, chuyen doi sang bat phan so thap phan 175 nhir sau:

0 2 (so dir thu* 3)

8) 2 5 (so du1 thu* 2)8)21 7 (so du* thu* nhat)8)175

Viet gon lai nhir sau:

Voi cac so phan cua he bat phan, phep nhan thay the cho phep chia va viet

so nho vao phan nguyen Vi du, chuyen doi phan phan cua so thap phan 0,23 thanh phan phan cua so bat phan:

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0,23 x 8 = 1,84 = 0,84 vdi so nh6 la 1

0,84 x 8 = 6,72 = 0, 72 vdi so nhd la 6

0,72 x 8 = 5,76 = 0,76 vdi so nhd la 5

oo-

*o'«Do

V V

Cac so nhd doc theo chieu xuong cho phan phan cua so bat phan Neu doi hoi co do chi'nh xac cao hon, ta tiep tuc nhan se diroc nhieu con so bat phan hon.Ket qua la: 0,2310 = 0,1658

? 9

- Chuyen doi bat phan - nhj phan

Vi 8 (co so cua he bat phan) la luy thira 3 cua 2 (co so cua he nhi phan), nen

ta co the chuyen doi tir bat phan sang nhi phan bang cach chuyen moi so bat phan sang so nhi phan tirong dirong

+ Vi du, chuyen so bat phan 43 thanh so nhi phan tirong dirong nhir sau:

O day, moi so bat phan chuyen sang nhi phan tirong dirong (4 tro thanh 100,

3 tro thanh 011) So nhi phan 100 011 tirong dirong voi so bat phan 43 thirdng thi

bo khoang trong giira cac nhom 3 bit, dieu do lam cho viec doc so nhi phan de dang hon

+ Mot vi du khac, mot so bat phan diroc chuyen thanh nhi phan nhir sau:

Ket qua la: 35748 = 01 11 011 1 1 1002

+ Mot vi du khac: khong kho khan gi khi chuyen so bat phan hdn hop (ca phan nguyen Ian phan phan) sang so nhi phan tirong dirong So bat phan 34.562 trd thanh:

Ket qua la: 34,5628 = 011100.1011100102

- Chuyen doi nhi phan - bat phan

Chuyen doi tir nhi phan sang bat phan la thirc hien ngiroc lai thu tuc trirdc day De dang nhd lai rang moi nhom gom 3 bit, b£t dau tinh tir dau phay nhi phan roi chuyen moi nhom thanh so bat phan tu'Ong dirong (them so 0 vao moi dau cua

day nhi phan cho day nhom neu can thiet) Vi du, so nhi phan 1011,01101 chuyen nhir sau:

So bat phan hon hop

Bat dau tif dau phay nhi phan, thu’c hien theo hai hirdng, tach cac bit thanh nhom 3 Trong trirdng hop nay, them cac so 0 de cac nhom ben ngoai cung diroc day 3 bit Chuyen moi nhom thanh so bat phan tuting di/Ong

Ket qua la: 1011,011012 = 13,328

Viec chuyen doi de dang tis bat phan thanh nhi phan va ngiroc lai co nhieu iru

viet vi lay tin ra hoac cho tin vao he thong digital it doi hoi ve cau true mach vi chung de dang doc va in ra so bat phan hon la so nhi phan

Mot iru viet khac nira la cac so thap phan Idn diroc chuyen doi de dang sang nhi phan neu trirdc het chuyen sang bat phan, roi sau do chuyen sang nhi phan

Vi du: chuyen doi so thap phan 363 thanh so nhi phan

Tri/dc het doi sang bat phan

0545

8) 363

553

oo-

*o

=3

-<Q)_COTiep theo, doi so bat phan 553 thanh so nhi phan tirong dirong:

Ket qua la: 36310 = 5538 = 1011010112

1.5 SO THAP LUC PHAN

So thap luc phan diroc sir dung rong rai doi vdi (iP Trirdc het, so thap luc phan ngan hon so thap phan Dieu do lam cho de viet va de nhd cac so thap luc phan Hon nura, ta co the nham moi khi chuyen sang he nhi phan

He thap luc phan co co so 16, co tat ca 16 con so tir so 0 den so 9, tir A den

F Noi mot cach khac, sau khi dem den so 9 trong he thap luc phan, ta tiep tuc dem nhir sau:

15

- Chuyen doi thap luc phan - nhj phan

Muon chuyen doi mot so thap luc phan sang so nhi phan, ta chuyen doi moi con so thap luc phan thanh 4 bit tirong di/Cng khi dung ma ghi trong Bang 1.2: So thap luc phan va cac so thap phan, nhi phan tirong dirong"

Vi du, chuyen so thap luc phan 9 A F thanh nhi phan, ta thirc hien nhir sau:

- Chuyen doi nhj phan - thap luc phan

Chuyen doi ngiroc lai, tir nhi phan sang thap luc phan, ta lai dung ma trong

Bang 1.2 O day co 2 vi du,

+ So nhi phan 1000 1100 chuyen sang thap luc phan nhir sau:

▼8

▼C+ So nhi phan: 1110 1000 0110 chuyen sang thap luc phan nhir sau:

Bang 1.2: So thap phan va

cac so thap luc phan, nhi phan tirong dirong

s 6 th A p phan s 6 th A p luc ph A n s6 NHI ph A n

- Chuyen doi thap luc phan - thap phan:

Chuyen doi so thap luc phan sang thap phan nhir the nao? Trong he thap luc phan, moi vi tri con so ti/Ong ifng vdi luy thira c0 16 trong so cua cac vi tri so trong he thap luc phan nhir sau:

163 162 161 16° , 16“ 1 16~2 16-3

Dau phay thap luc phan

Do do, de chuyen doi tir thap luc phan sang thap phan, ta nhan moi con so thap luc phan vdi trong so cua no, roi cong tat ca cac ti'ch lai vdi nhau

Vi du, so thap luc phan F 8 E 6 , 3 9 chuyen sang thap phan nhir sau:

F 8 E 6 , 3 9 = F x (163) + 8 x (162) + E x (161) + 6 x (16°)+ 3 x (16~1)+ 9 x(16“2)

= 15 x (163) + 8 x (162) +14 x (161)+ 6 x (16°)+ 3 x (16~1)+ 9 x (16~2)

= 61.440 + 2048 + 224 + 6 + 0,1875 + 0,0352

= 63.718,2227

- Chuyen doi thap phan - thap luc phan

Cach chuyen doi thap phan - thap luc phan bang cach chia lien tiep cho 16, ghi lai cac so dir tirong tir nhir cac cach doi thap phan sang nhi phan va bat phan tren day

Vi du, chuyen doi so thap phan 2479 thanh so thap luc phan nhir sau:

XD

13

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1.6 MA ASCII

De xuat nhap tin tir may vi ti'nh, ta can vai loai ma so alpha (loai ma cho cac chCr, cac so va cac ky tir khac) Co mot thdi, cac nha san xuat da dung cac ma so alpha rieng cua minh, dan den sir roi loan trong viec san xuat, vi nhieu loai ma khac nhau diroc dung vao viec xuat nhap tin Trong cong nghiep tin hoc, ngirdi ta

da thong nhat dung ma ASCII (ASCII: American Standard Code for Information Interchange) Ma nay cho phep nha san xuat tieu chuan hoa phan cCrng cua may

vi ti'nh nhir ban phim, may in va man hinh

- Sur dung ma ASCII

Ma ASCII (doc la as-ki) la ma 7 bit x6, x5, x4, x5, x4, x3, x2, x1t x0, trong do x la

so 0 hoac so 1 Vi du, chCr A di/pc ma hoa la: 1000001, de de doc, ta viet 100

Vi du, chCr A co day bit x6 x5 x4 la 100 va day bit x3 x2 x1 xO la 0001 Do do, ma ASCII la: 100 0001 (A)

Bang 1.3 co so ma cho chCr thirdng ChCr a co ma la: 110 0001 (chuf a)

Cac vi du khac la: 110 0010 (chCr b); 110 0011 (chCr c) v.v

Trong BANG 1.3 cum SP thay cho khoang trang (space) Go vao thanh SP

cua ban phi'm ASCII la nap vao may vi tinh ma 010 0000 (space)

- Bit ch in le

Ma ASCII diroc dung de truyen tren dirong day dien thoai Nhir vay co the khi truyen dan gay ra sai loi Mot bit c h in le thirdng diroc sir dung de truyen dan cung vdi cac bit goc de phat hien cac sai loi Mot bo kiem tra bit chan le d dau thu co the kiem tra bit chan va bit le xem co trung hop vdi bit c h in bit le da dirpc sap xep trirdc d may phat va may thu hay khong

Vi ma ASCII co 7 bit, them mot bit chan le de tao nen so lieu diroc truyen di la

8 bit, co ki'ch cd sau:

x7 X6 X5 X4 X3 X2 Xt x0

/*

bit chin, bit le

Day la do dai ly tirong vi hau het thiet bi digital diroc xac lap de truyen di cac byte (8 bit) so lieu

1.7 MA D J 3

Ma dir 3 la ma 4 bit quan trong, thirdng dupe dung vdi ma BCD De chuyen doi so thap phan nao do thanh dang ma dir 3, them 3 vao mdi con so thap phan, roi chuyen do’i tong do thanh so nhi phan 4 bit

Vi du, chuyen do’ i so thap phan 12 thanh ma du1 3 Trirdc het cong them 3 vao moi con so thap phan:

+ 3 + 3

1.8 MA G R A Y

Bang 1.4 gidi thieu ma GRAY, tirong Crng vdi so nhi phan Moi so cua ma

GRAY khac vdi so trudc 1 bit Vi du, d so thap phan tir 7 den 8, so ma GRAY thay

19

doi tir 0100 den 1100, cac so nay chi khac 6 bit co trong so Idn nhat (MSB) Nhi/ trong mot vi du khac, so thap phan 13 va 14 dupe chuyen doi thanh ma GRAY la

1011 va 1001; cac so nay chi khac mot vi tri so (vi tri thu1 hai ke tir ben phai) Nhir vay, trong toan bo ma GRAY, moi so chi khac 1 bit v6i so trirdc

Ngoai ma du” 3 va ma GRAY, con co nhieu loai dang ma nhi phan, nhir ma BCD, ma nay con dirpc goi la ma 8 4 2 1

CAU HOI VA BAI TAP

1.1 Bieu dien mot so trong he dem thap phan dtidi dang luy tnira.

1.2 Trong so la gi?

1.3 Vi tri cac con so trong day so la gi?

1.4 Cho vi du ve he dem thap phan dudi dang luy thu’a Xac dinh vi tri cac

con so, trong so va he so cua day so do

1.5 Cho vi du ve he dem nhi phan.

1.6 Bieu dien he dem nhi phan trong cau hoi 5 dirdi dang luy thu’a cd so 2 1.7 Neu i/u diem va nhUdc diem cua he nhi phan.

1.8 Mot Nibble co bao nhieu bit?

1.9 Hai Byte co bao nhieu bit?

1.10 The nao la LSD va MSD, cho vi du?

1.11 Trong ngon ngCrdung a he nhi phan, IK, 2M, 1G la gi?

1.12 Co the doi so nhi phan sang bat phan b ln g cach ghep cac ky so thanh

nhom moi nhom co bao nhieu bit?

1.13 Co the doi so nhi phan sang thap luc phan bang cach ghep cac ky so

thanh nhom, moi nhom co bao nhieu bit?

1.14 De bieu dien cung mot gia tri cua so thap phan vi du so 2004 so co co

so ion hay nho can it con so nhat (do dai so ngan nhat)?

1.15 Chuyen doi nhi phan sang than nhan va ngiroc lai viec chuyen doi nao

de thu’c hien hon?

1.16 Cac kv tir dude ma hoa trong he thong ma ASCII nhir the nao?

1.18 May tinh the he hien dai hoat dong theo he bao nhieu bit?

1.19 So nhi phan dirdi day co bao nhieu bit, bao nhieu Nibble va bao nhieu Byte?

1.21* Doi cac so nhi phan trong bang dirdi day ra cac so thap luc phan, thap

phan va bat phan:

C H U O N G 2

CAC CONG LOGIC,

D A I SO LOGIC, PHAN TICH

■

V A TONG HOP MACH LOGICa ■

Hoc xong chwong nay, hoc vien co kha nang:

□ Hieu di/oc cac dac trung cua cac cong logic:

Invectd (cong dao), OR, AND, NOR NAND, X-OR, va X-NOR,

□ Xay di/ng di/dc cac mach logic theo cac bang st/

that

□ Ap dung cac he thC/c logic, cac phi/dng phap tong

cua tich va tich cua tong de toi i/u cac mach logic

□ Ap dung phwong phap Karnaugh de toi i/u mach

logic.

TONG QUAN

Chirong nay thao luan ve cac cong logic, nhir cac cong INVECTO (cong dac), AND, OR, NAND, NOR , dong thdi thao luan ve cac bieu thu’c dai so logic, nhCrng he thu’c dai so Boole va hai dinh ly De Morgan

Chirong nay cung nghien ciru cac phirong phap gian iroc mach logic bang cac phuo'ng phap tong cua tich, tich cua tong va bang phirong phap Karnaugh

23

2.1 CONG DAO (iNVECTO )

- Vi sao sudung hoat dong hai trang thai?

Hoat dong hai trang thai la hoat dong rat thudng gap trong cac thiet bi dien tir digital, vi day la cach hoat dong co do tin cay cao cua tranzito va cac thiet bi chuyen mach khac Voi hoat dong hai trang thai, tat ca cac tin hieu de dang diroc nhan biet vdi hai trang thai hoac 6 mud dien ap thap hoac 6 mire dien ap cao Dieu don gian nay co y nghia quan trong de xay dung cac mach may tinh va cac thiet bi

ky thuat so khac co do tin cay, vi cac linh kien tich cuc chi can xuai hien hai trang thai: hoac dong hoac mo

- Surdung tranzito lam khoa chuyen mach

Dung tranzito lam chuyen mach, co nghia la sir dung dac tinh dan bao hoa va ngirng dan cua tranzito Khi dan bao hoa, tranzito diroc coi nhir la mot khoa chuyen mach dan dien (kin mach) Khi tranzito ngirng dan, no dude coi nhir khoa chuyen mach bi ho (hd mach) Nhir vay, tranzito co 2 trang thai hoat dong: kin mach va ho mach

• Mach cuc phat chung (Emito chung): Mach gidi thieu tren Hinh 2.1a la

mach Emito chung Dong lb bang:

Duong tai: Hinh 2.2 bieu thi dirong tai DC va AC Khi Vin b ln g 0 tronq

Hinh 2.1, tranzito d trang thai cat mach va diem hoat dong o' dau dirdi cua dirong

tai Trong trirdng hdp nay tranzito dude xem nhir mot chuyen mach ho circ adz -

cu t phat (Colecto va Emito) Mat khac khi V „ Idn tranzitd o' che do bao hoa va diem hoat dong 0 dau tren cua dudng tai mot cach ly tudng tranzito diroc xem nhu mot chuyen mach kin mach

(2.3)+ V c c

Bao hoa cirng: Bao hoa cirng co nghia la tranzito co dong ciTc goc (ci/c

Bado) du Ion de tranzito hoat dong 6 dau tren cua dudng tai Dan bao hoa mem khong du tin cay trong hau het cac truong hop vi co sir bien thien cua pdc (cung

giong nhir hFE) Mach trong che do bao hoa mem co the de dang chuyen sang che

do bao hoa vi ly do thay doi nhiet do hoac thay the tranzito

• Bao hoa curig co nghia la tranzito co dong 011*0 goc du Idn de di/Oc bao hoa du’di moi dieu k.ien hoat dong De co diroc bao hoa cirng, ngi/di thiet ke tinh toansao cho c bao hoa3 idn gap xap xi 10 Ian gia tri cua IB bao hoa Ti so 10:1 du nho dehau het cac tranzito duy tri bao hoa trong moi tri/dng hop nhi/ nhiet do tang qua, thay the tranzito hoac thay doi dien ap cung cap

Rc

Vi du dien ao vao V , tren Hinh 2.3 hoac la 0V hoac la +5V Khi V m bang 0V,

tranzito cat mach va luc do Vout bang +5V Khi Vin bang +5V tranzito hoat dong d che do bao hoa cirng, va Vou, xap xi bang 0 Trong trirdng hop nay lc bi0 hoa , ly tirong, la bang 5mA Bo qua gia tri VBEcua tranzito, lEba0hoa xap x' bang 0,5mA Do

do, ti so dong lcb3ChCa/lBbaohoa xap xi bang 10:1

Khi dien ap ngo vao circ dai bang dien ap cung cap tranzito co the dat diroc che do bao hoa cu'ng do sir dung ti so xap xi 10:1 doi vdi RB/R; Vi du RB = 10 kQ,

va R = 1 kQ, nhir trong Hinh 2.3: ti so cua RB/R- b ln g 10 vi vay tranzito hoat

dong d che do bao hoa cu’ng Vdi cac gia tri khac, chang han nhu' RB = 47 kQ va

Rc = 4,7 kQ, tranzito cung van hoat dong d che do bao hoa cu'ng vi ti so RJR

bang 10

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- Invectd dung tranzito

Bat ky Invecto nao cung chi co mot ngo vao va mot ngo ra Dirge goi la Invecto la vl trang thai 0 ngo ra luon luon trai ngiroc voi trang thai 6 ngo vao Dien hinh la khi dien ap ngo vao 6 muO dien ap cao (H) thi dien ap 6 ngo ra 6 muC dien

ap thap (L) Ngiroc lai, khi dien ap ngo vao 6 mCrc dien ap thap (L) thi dien ap ngo

ra o mCrc dien ap cao (H)

Hinh 2.3 la mot vi du cua Invecto ^Vi dien ap ngo vao chi co the co hai gia tri:

(OV hoac + 5V), tranzito hoac ngirng dan hoac dan bao hoa Vi vay, ta nhan dirge hai trang thai hoat dong, dieu do co nghia la dien ap ngo ra chi co hai gia tri on dinh (gia tri cao hoac gia tri thap)

Bang 2.1 tom tat hoat dong cua mot Invecto va dirge goi la bang si/ that (con

goi la bang chan ly) Bang si/ that la bang chi ra tat ca cac kha nang xay ra 0 ngo vao, ngo ra cua mach logic Ngo vao 0 mC/c dien ap thap co ti/ong Crng ngo ra 6 muO dien ap cao va ngo vao 0 m ut cao co ti/o'ng ting ngo ra 6 mtic thap Ngo ra Invecto cGng dirge goi la phan bu cua ngo vao Invecto

Bang 2.1: Invecto

- Ky hieu cua Invecto

Dung tranzito tren Hinh 2.3 la cach don gian nhat xay di/ng mot Invecto Co

nhieu cach thiet ke de tao nen Invecto co tro khang vao va tro khang ra di/gc cai

thien Hinh 2.4a la ky hieu cua Invecto Doi khi 6 mot so so do mach, ngi/di ta

dung ky hieu tren Hinh 2.4b mat ngdng (vong tron nho) nam o phia ngo vao Khi

nao ta thay mot trong hai ky hieu nay can nho rang ngo ra la phan bu cua ngo vao

Hinh 2.5 gidi thieu IC 7404 la IC TTL Day la IC digital, 14 chan, dang DIP

(Dual in line package: IC hinh hop, co 2 hang chan), co 6 cong Invecto Chan 14 ket noi vdi nguon cung cap + Vcc va chan 7 ket noi v6i dat GND

Hinh 2.4a: Ky hieu cong Invectd Hinh 2.4b: Cach ky hieu khac cua cong Invectd

:

2.2 CONG HOAC (OR)

Mot cong OR co hai hoac nhieu ngo vao cua tin hieu nhi/ng chi co mot ngo

ra Dirpc goi la cong OR vi dien ap ngo ra 0 mtic cao (H) neu mot hoac tat ca cac dien ap 6 ngo vao deu 6 mtic cao (H) Vi du, ngo ra cua cong OR hai ngo vao dat mtic cao neu mot trong hai ngo vao hoac ca hai ngo vao deu 0 mtic cao

Himh 2.6a bieu thi cach xay di/ng cong OR hai ngo vao va Hinh 2.6b don

gian hoa cach ve cua Hinh 2.6a Cac dien ap ngo vao dirpc ky hieu la A va B va

dien ap ngo ra dupe ky hieu la Y Hay gia du cac dien ap ngo vao hoac la OV (mtic thap L) hoac la +5V (mtic cao H) Chi co 4 trifdng hop xay ra:

Trudng hop 1: A 6 mtic thap va B cung 6 mtic thap Vdi hai ngo vao cung 0 mtic thap, dien ap ngo ra cung a mtic thap vi ca hai diot deu khong dan Do do, Y

0 mtic thap L

Truong hop 2: A 6 mtic thap con B 6 mtic cao’ H Dien ap ngo vao B 6 mtic cao (+5V), diot dirdi co thien ap thuan, dan den dien ap 6 ngo ra dat mtic ly ti/dng

la +5V, hoac xap xi +4,3V, neu co ti'nh den dien ap dat tren diot Du dien ap ngo

ra Y 0 mtic +5V hoac +4,3V thi dien ap ngo ra Y van 0 mtic cao Chu y rang, diot tren co thien ap ngi/pc

Truong hop 3: A 6 mtic cao con B 6 mtic thap Vi ti'nh doi xting cua mach, nen mach hoat dong tirong tir nhir 6 trudng hop 2 Diot tren 0 trang thai dan con diot diroi 6 trang thai ngirng dan, dien ap ngo ra Y o mtic cao

Trudng hop 4: A 6 mtic cao va B cung 6 mtic cao Voi ca hai ngo vao deu co dien ap o mtic cao (+ 5V), ca hai diot deu co thien ap thuan Vi dien ap ngo vao mac song song, dien ap ngo ra dat mtic ly ti/dng la + 5V Do do Y dat mtic cao (+ 5V)

- Bang sir that

Bang 2.3 la bang sti that bieu thi du'di dang nhi phan Khi xem xet bang nay

ta thay co lien quan den Bang 2.4, H la mtic dien ap cao (High) +5V, co ma la 1;

L la mtic dien ap thap (Low) 0 V, co ma la 0

Tom lai, qua moi quan he gitia trang thai ngo rs vdi trang thai ngo vao, cong

OR la cong co dien ap ngo ra o' rntic 1 khi mot hoac tat ca cac ngo vao 6 mtic 1

Bieu thi bang mtic dien Bieu thi bang so nhi phan

Ky hieu logic

Hinh 2.7: Cac cong OR a) 2 ngo vao; b) 3 ngo vao; c) 4 ngo vao

Doi vdi cac cong OR nay, ngo ra se 0 mu’c 1 neu mot hoac mot vai hoac tat

ca cac ngo vao 0 mu’c 1 Chi co mot cach de ngo ra 6 mu’c 0 la tat ca cac ngo vao deu 0 mu’c 0

- Cong OR TTL

Hinh 2.8 la so do chan IC 7432, loai IC TTL co 4 cong OR 2 ngo vao Day la

IC digital, 14 chan, dang DIP (Dual in line package: IC hinh hop, co 2 hang chan) Sau khi noi chan 14 vdi nguon cung cap Vcc (+ 5V), va noi chan 7 vdi dat GND, ta

co the noi mot hoac nhieu cong OR vdi cac IC TTL khac

Hinh 2.8: So do chan IC 7432

- Bieu do thdi gian

Hinh 2.9 la bieu do thdi gian cua cong OR 2 ngo vao Cac dien ap vao dUOc

dira den chan 1 va 2 cua IC 7432 Chan 3 6 mu’c 0 chi khi ca hai ngo vao deu d mu’c

0 Ngoai dieu kien tren, ngo ra co mu’c 1 vi mot hoac ca hai chan deu o mu’c 1

Hinh 2.9: Bieu do thdi gian

2.3 CONG VA (AND)

- Cong AND 2 ngo vao

Cong AND co ngo ra d mtic 1 chi khi tat ca cac ngo vao 6 mtic 1

Hinh 2.10a chi ra cach xay dting cong AND 2 ngo vao Hinh 2.10b la cach ve

gian udc cua Hinh 2.10a Cac dien ap vao co ten la A va B, dien ap ngo ra co ten

la Y Gia dinh rang dien ap cung cap la + 5V Ta cung gia dinh rang cac dien ap ngo vao hoac la 0V hoac la + 5V Chi co 4 trudng hop xay ra 6 ngo vao:

+ Vcc

Trudng hap 1: A = 0, B = 0, ca hai dien ap ngo vao deu 6 mUc 0 Catot cua moi diot dupe noi dat Do do, ca hai diot dupe phan cUc thuan va noi song song Vi vay, dien ap ngo ra ly tudng bang 0 (xap xi bang 0,7 V) Dieu do co nghia la Y = 0

Trudng hap 2: A = 0, B = 1 Vi A = 0, nen diot phi'a tren dupe phan cuc thuan,

day dien ap ngo ra xuong mUc 0 Vi ngo vao B = 1, nen diot phi'a du6i co phan cuc ngupc Do do, dien ap ngo ra ly tudng bang 0V (hoac xap xi bang 0,7V), Y = 0

Trudng hap 3: A = 1, B = 0 Vi mach doi xUng, nen mach hoat dong tuong tu

trudng hop 2 Diot phi'a tren ngung dan, diot phi'a dudi dan, Y = 0

Trudng hap 4: A = 1, B = 1, ca hai ngo vao deu bang +5V, ca hai diot deu

khong dan Vi cac diot deu ngung dan, khong co dong chay qua R , va ngo ra

dupe keo len dien ap cung cap (+5V), Y = 1.

- Bang su that

Bang 2.4 la Bang suthat cu3 cong AND 2 ngo vao Khi xem xet bang suthat

ta thay cong AND co ngo ra Y = 1 chi khi A = 1 va B = 1 Noi cach khac ngo ra

Y = 1 chi khi tat ca cac ngo vao co mUc dien deu bang 1

29

Bang 2.4: Cong AND 2 ngo vao Bang 2.5: Tiidng di/ong nhi phan

- Cong AND 3 ngo vao

Khi tat ca cac ngo vao 6 mu’c 0, tat ca cac ngo vao deu dan, do do ngo ra

Y = 0 Ngay khi chi co mot ngo vao a mu’c 0, Y cGng bang 0, vi diot dirge noi voi

ngo vao 6 mu’c 0 se 6 trang thai dan Chi co mot kha nang de ngo ra 6 mu’c 1 la tat

ca cac ngo vao deu O mu’c 1 (+ 5V) Khi do tat ca cac diot deu ngung d in va dien

ap cung cap (+ 5V) keo ngo ra len trang thai 1

- Cac cong AND TTL

Sau khi noi dien ap cung cap +5V vao chan 14 va tiep dat chan 7, ta co the noi mot cong hoac cac cong AND vdi cac IC TTL khac

- Bieu do thdi gian

Hinh 2.13 la bieu do thdi gian cua cong AND 2 ngo vao Cac dien ap ngo vao

dira den chan 1 va 2 cua IC 7408 Chan 3 la ngo ra 6 mu’c 1 chi khi ca 2 chan ngo vao deu 6 mu’c 1 (giCra cac thdi diem C va D, G va H v.v ) Ngo ra 6 mUc 0 doi v6i cac khoang thdi gian con lai

Chanl

Chan2

Chan3

2.4 CONG HOAC-OAO (NOR)

- Ky hieu cong NOR

Mach logic 6 Hinh 2.14 dirpc goi la cong NOT-OR vi ngo ra bang:

Y = A + BBieu thirc tren doc la "Y bang NOT cua A OR B", hoac "Y bang phan bu cua

A OR B" Vi mach la cong OR dirpc noi tiep voi cong dao, cach duy nhat de co ngo

ra bang 1 la ca hai ngo vao deu 6 mu’c 0, nhir da chi ra 6 Bang 2.7.

Mach logic 0 Hinh 2.14b la ky hieu cua cong NOR Vong tron nho 6 ngo ra nhac ta nhd phai dao sau cong OR Tu’ NOT-OR dirpc rut gon la NOR V6i cong NOR, tat ca cac ngo vao phai 0 mu’c 0 de dat 0 ngo ra co mCrc 1 Neu ngo vao nao

do 6 mu’c 1 thi ngo ra 0 mCrc 0

2.5 CONG VA-OAO (NAND)

Mach logic 6 Hinh 2.15b la ky hieu cua cong NAND Dau tron nho 6 ngo ra nhac ta nhd dao sau co’ng AND TCr NOT-AND dirpc rut gon la NAND Vdi cong NAND tat ca cac ngo vao deu d mCrc 1 thi ngo ra d mCrc 0 Neu ngo vao nao do d mCrc 0, thi ngo ra se d mu’c 1

- Cong NAND TTL

IC 7400 co 4 co’ng NAND 2 ngo vao Vi co’ng NAND dong vai tro trung tam trong cong nghe TTL, nen ngay nay cong NAND di/pc dung rong rai nhat va gia thanh ha nhat Hon nCra, co’ng NAND co nhieu dang cau tao hon cac loai cong

khac, nhir Bang 2.9 da chi ra Co’ ng NAND co cac loai 2, 3, 4, hoac 8 ngo vao Cac cong khac co it dang cau tao hon, vi du, cong OR chi co moi loai 2 ngo vao (IC 7432)

2.6 CONG X-OR

Cong X-OR chi'nh la cong Eclusive - OR (con goi la cong OR loai trif), co ngo

ra 0 mu’c 1 chi khi so le ngo vao 6 mu’c 1 Hinh 2.16 gidi thieu cach xay di/ng cong

X-OR

Cong AND phi'a tren co ti'ch A B, cong AND di/6i co ti'ch A B Do do, ngo ra cua cong OR la:

Y = A B + A BDieu gi se xay ra khi co cac chan khac mu’c logic? Khi A va B cung 6 mu’c 0,

ca hai cong AND co ngo ra 0 mu’c 0, do do Y = 0 Neu A = 0, B = 1, cong AND tren

6 mu’c 1, nen cong OR co ngo ra Y = 1 Tirong tu”, chan A = 1, B = 0 ket qua cuoi cung la Y = 1 Neu ca hai ngo vao deu 6 mu’c 1, ngo ra cua ca hai cong AND deu

6 mu’c 0 va cuoi cung Y = 0

Bang 2.10 la bang sir that cua cong X-OR 2 ngo vao Ngo ra d mu’c 1 khi mot

trong hai ngo vao A va B d mu’c 1, khi ca hai ngo vao cung d mu’c 0 hoac mu’c 1 thi ngo ra d mu’c 0 Tom lai, ngo ra bang 1 chi khi hai ngo vao khac mu’c nhau

Hinh 2.17 la ky hieu cong X-OR 2 ngo vao.

Bang 2.10: Bang sir that cong X-OR

- Cong X-OR 4 ngo vao

Hinh 2.18 la hai cong X-OR dieu khien mot cong X-OR Neu tat ca cac ngo

vao (A, B C D) deu d mu’c 0, cac ngo vao co cac ngo ra d mu’c 0 nen loi ra cua cong cuoi cung d mu’c 0 Neu cac ngo vao A, B C d mu’c 0 con D d mu’c 1, nhir vay cong X-OR d phi'a tren co ngo ra d mu’c 0, cong X-OR duoi co ngo ra d rnirc 1

va ngo ra cuoi cung d mu’c 1

Hinh 2.18: Cong X-OR 4 ngo vao Bang 2.11: Cong X-OR 4 ngo vao

Neu tiep tuc phan tich cac hoat dong cua mach vdi cac ngo vao con lai, ta co

the thiet lap di/dc Bang 2.11 Tu” Bang 2.11 ta co nhan xet quan trong la so le cac

ngo vao d muC 1 se cho ngo ra 6 mu’c 1 Vi du, cac ngo vao dau tien ABCD = 0001 tao nen ngo ra bang 1, vi co so le ngo vao co mu’c 1 Cac ngo vao khac tao nen ngo ra bang 1 la: ABCD = 0010; 0100; 1000; 1110; 1101; 1011; 0111

Hinh 2.18 minh hoa cong X-OR 4 ngo vao Nhin ky hieu nay ta nho ngay

rang cong X-OR se cho ngo ra d mu’c 1 khi trong so cac ngo vao A, B, C, D co so

le ngo vao d mu’c 1

2.7 DAI SO LOGIC

- Tong quan

Mot hanh dong, mot ket luan dung hay sai, mot chuyen dong nhanh hay cham, cac hien tirpng ty nhien, xa hoi va ca nhCrng y ngh? cua chung ta doi hoi cau tra loi co hai trang thai nhu” tren Logic hai trang thai da co anh hirdng sau sac, Aristote da de ra phirong phap chuan xac de dat chan ly Sau nay, logic da thu hut sir chu y cua cac nha toan hoc Augustus De Morgan la ngirdi da tim ra moi lien he chat che giCra logic va toan hoc Nhirng G Boole (1854) la ngirdi da phat minh ra

loai dai so m6i, thay the phirong phap cua Aristote Trong gan mot the ky, dai so Boole chi/a co tac dong den ky thuat va cong nghe, mai den nam 1938, Shannon

ap dung dai so Boole vao viec mo ta cac mach dien cua tong dai dien thoai Nho cac cong trinh cua Shannon, ve sau nay, cac nha ky thuat da dung dai so Boole

de phan ti'ch va thiet ke cac mach vi tinh

Y = NOT ANeu A = 0 thi:

Y = NOT 0 = 1Mat khac, neu A = 1 thi:

y = NOT 1 = 0Trong dai so Boole, dau gach tren thay the cho toan tir NOT Nhir vay, phirong trinh logic (2.4) co the viet thanh:

Bieu thu’c (2.5) dirpc doc la "Y bang NOT A", hoac "Y bang phan bu cua A" Bieu thu’c (2.5) la cach viet chuan cho ngo ra cua mot cong NOT

- Toan tur OR

Mot cach de bieu thi hoat dong cua cong OR (Hinh 2.20), phirong trinh logic

dirpc viet nhir sau:

Phirong trinh logic noi len rang ngo ra dirpc xac dinh bang luat OR cua cac ngo vao Vi du, neu A = 0, B = 0 thi:

Y = A OR B = 0 OR 0 = 0Mot vi du khac, neu A = 1, B = 0, thi:

Y = A OR B = 1 OR 0 = 1Tirong tir, neu A = 0, B= 1, thi:

Y = A OR B = 0 OR 1 = 1

Trong dai so Boole, dau + thay cho toan tir OR Nhir vay,

viet lai la:

Y = A + BBieu thirc tren doc la "Y bang A OR B" Bieu thu’c (2.7) la

ngo ra cua cong OR

bieu thu’c (2.6) dirpc

(2.7)cach viet chuan cho

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- Toan tur AND

Phirong trinh viet cho cong AND 6 Hinh 2.21 la:

Bieu thu’c (2.9) la cach viet chuan cho ngo ra cua cong AND

Neu ca hai ngo vao cua cong AND deu 6 mire 0 thi:

- Cac phi/dng trinh dai so Boole cua cac mach logic

Ta co the dung cac dau + cho cac cong OR dau x (hoac dau cham hoac bo dau cham va viet lien sat nhau) cho cac cong AND dau gach tren cho cac c6ng dao (NOT) de viet phirong trinh cac mach logic Noi cach khac ta co the sir duno dai so Boole de viet cac phu'o'ng trinh mach logic voi cac ky hieu tren day V' du

Hinh 2.22 ve hai tang cac cong OR dung !C 7432 Ngo ra cua cong OR dau tien

la:

Y3 = A + BChi so dudi 3 cua Y la so thu” tu chan IC theo qui dinh Ngo ra cua cong OR thu* hai la:

Y6 = Y3 + C = A + B + CNgo ra cuoi cung la:

y8 = y6 + d = a + b + c + d

Dieu do noi len rang mach logic tren Hinh 2.22 tirong dirong cong OR 4 ngo

vao, thirc hien luat OR de cho ket qua ngo ra cuoi cung

IC 741 I la loai IC TTL, dang DIP 14 chan, gom 3 cong AND 3 ngo vao Thong thirdng dien ap cung cap (+ 5V) dilOc noi voi chan 14 va tiep dat 0 chan 7

Hinh 2.22 la mach logic noi hai cong AND 3 ngo vao cua IC 7411 Bay gid hay viet

phirong trinh dai so Boole cho ngo ra cuoi cung

Ngo ra cua cong AND dau la:

Y12 = A B CDay la mot ngo vao cua cong AND thir hai, ngo ra cuoi cung la:

Y6 = Y12 D E = A B C D E

Do do, mach tirong dirong voi cong AND 5 ngo vao

2.8 HAI BjNH LY DE MORGAN

- Cong AND dao ngo vao

thirdng ve nhir Hinh 2.23 Vong tron nhd d ngo vao nhac ta nhd dao trirdc khi thirc

hien toan tir AND Hay phan tich mach logic nay doi vdi tat ca cac kha nang co the xay ra d ngo vao

Trudng hap 1: Neu A = 0, B = 0, cac cong dao tao nen d ngd vao cong AND

co mu’c 1 Do do, Y = 1

Trudng hap 2: Neu A = 1, B = 0, cong dao tren tao nen d ngd vao cong AND

co mu’c 0, ket qua la Y = 0

Trudng hap 3: Neu A = 0, B = 1 cong dao di/di tao nen d ngd vao cong AND

cd mu’c 0, ket qua la Y = 0

Trudng hap 4: Neu A = 1, B = 1, cac cong dao tao nen mu'c 0 d ngd vao cong

AND, do do Y = 0

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i O - £ > = D

-B

Bang 1.12: Cong AND dao ngo vao

- Kha nang thay the

Bang 2.12 la bang su' that cua mach logic trong Hinh 2.23b So sanh vdi

bang su'that cong NOR (Bang 2.7), ta thay hai bang co gia tri nhu nhau Dieu do

co nghia la cong AND dao ngd vao cho cung gia tri 6 ngo ra nhir 6 cong NOR Noi cach khac, cac mach co the tir chuyen doi Neu cho mot mach logic nao do 0 cong NOR, ta co the thay the moi cong NOR bang cong AND dao ngo vao Ngiroc lai, neu mot mach logic co cac cong AND dao ngo vao, ta co the thay the bang cong NOR Sau nay, cac vi du se chi ra rang cac cong NOR tirong dirong vdi cac cong AND dao ngo vao, cac cong nay co nhCrng Crng dung thuc tien

- Djnh ly De Morgan thu" nhat

Phirong trinh dai so Boole cho mach logic 0 Hinh 2.24 la:

Y = A + B

Phirong trinh dai so Boole doi vdi Hinh 2.23 la:

Y = A BPhUdng trinh tren mo ta cong NOR, phirong trinh dudi mo ta cong AND dao ngo vao Vi cac ngo ra dong nhat khi cung gia tri ngd vao Do do, ta co the viet

Sir dong nhat nay chinh la noi dung dinh ly De Morgan thir nhat Dinh ly do

la: "Phan bu cua m ot tong bang tich cua cac phan b u "

Hinh 2.24 neu len y nghia cua dinh ly De Morgan thir nhat.

Tir ket qua tren dan den mot nguyen tsic la bang sir that mach logic va phirong trinh dai so Boole ia nhCrng phu'ong tien khac nhau de xem xet cung mot van de Neu chung ta chung minh diroc rang cac bang su that la dong nhat, dieu

do noi len la cac mach logic tuong ting co the tu chuyen doi cho nhau duoc Khi phan tich, ta thudng xuat phat tU mach logic, xay dung bang su' that cua macn do tong quat hoa bang phu’Ong trinh dai so Booie Khi thiet ke, ta thu’dng xuat phat tu bang su’ that, xay dung phuong trinh dai so Boole va di den xay dung mach logic

- Cong OR dao ngo vao

Hinh 2.25 ve cong OR dao ngo vac Mach thirdng dupe ve don gian nhu” Hinh 2.25, cac vong tron nho dirpc coi nhir la phep dao Hay phan tich mach logic

vdi tat ca cac trirdng hop co the xay ra 0 ngo vao

Trudng hap 1: Neu A = 0, B = 0, cac cong dao tao nen cac ngo vao cong

OR 0 mu'c 1 Do do, Y = 1

Trudng hap 2: Neu A = 0, B == 1, cong dao tren tao nen mot ngo vao cong

OR o mire 1, nen Y = 1

Trudng hap 3: Neu A = 1, B =- 0, cong dao dudi tao nen mot ngo vao cong

OR 6 mu’c 1, ket qua la Y = 1

Trudng hap 4: Neu A = 1, B =: 1, cac cong dao tao nen 6 cac ngo vao cong

OR co mu’c 0, do do Y = 0

k r y

Bang 2.13: Cong OR dao ngo vao

- Kha nang thay the

Bang 2.13 la bang sir that cua mach logic tren Hinh 2.25 So sanh vdi Bang 2.8 ta thay hai bang nay dong nhat vdi nhau, dieu do co nghia la cong OR

dao ngo vao 6 Hinh 2.25 tao nen cung cac tin hieu ngo ra nhir cong NAND 6

NAND bang cong OR dao ngo vao Ngiroc lai, neu mach logic co cac cong OR dao ngo vao, ta co the thay the moi cong do bang mot cong NAND

Phirong trinh logic cua dai so Boole cho Hinh 2.15 la:

Y = AB

Phirong trinh logic cua dai so Boole cho Hinh 2.25 la:

Y = A + BPhirong trinh tren mo ta cong NAND va phirong trinh dirdi mo ta cong OR dao ngo vao Vi cac ngo ra cho ket qua dong nhat doi voi cung cac dieu kien dau vao Ta co the viet:

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Sir dong nhat nay chi'nh la noi dung dinh ly De Morgan thu1 hai Dinh ly diroc

phat bieu nhu sau: "Phan bu cua m ot tich b in g tong cac phan b u "

Hinh 2.26 neu len y nghia cua dinh ly De Morgan thu’ hai.

2.9 CAC DINH LUAT VA DINH LY CUA DAI SO BOOLE ■ ■ ■ ■

- Cac dinh luat co ban

Dinh luat nay rat de nho vi no gidno dai so thong thirdng

Hinh 2.27e cho thay hai mach logic tirong sing bang nhau Dinh luat phan phoi goi y cho ta ve gia tri cua dai so Booie Neu ta sap xep trirdc mot bieu thirc dai so Boole, cac mach logic tirong ung co the don gian hon Chung ta co the sir dung cac dinh luat nay de gian irdc nhting bieu thu’c ohCrc tap cua dai so Boole va dat diroc mot mach logic don gian non