Slide 1 1 Lecture DIGITAL SYSTEMS Chapter 5 Digital Arithmetic Operations and Circuits Assoc Prof Nguyen Thanh Hai, PhD HCMC University of Technical Education Faculty of Electrical & Electronic Engine[.]
Trang 1DIGITAL SYSTEMS
Chapter 5 Digital Arithmetic: Operations and Circuits
Assoc Prof Nguyen Thanh Hai, PhD
HCMC University of Technical Education
Faculty of Electrical & Electronic Engineering
Trang 2Faculty of Electrical & Electronic Engineering
Assoc Prof Nguyen Thanh Hai, PhD
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Assoc Prof Nguyen Thanh Hai, PhD
1 Cộng trừ nhị phân
2 Cộng trừ trong hệ thống bù 2
3 Cộng số BCD
Contents
Trang 3HCMC University of Technology and Education
Faculty of Electrical & Electronic Engineering 1 Binary Addition
0 0 1 1 (3)
0 1 1 0 (6)
1 0 0 1 (9)
010.110 (2.750)
1 10.001 (6.125) +
Cộng nhị phân
0 1 1 0 (6)
0 0 1 1 (3)
0 0 1 1 (3)
-0 0 1 1 (-3)
0 0 1 1 (3) +
Trang 4Faculty of Electrical & Electronic Engineering
Assoc Prof Nguyen Thanh Hai, PhD
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Addition in 2’s-Complement System
Bù 1 (1’s-Complement) Form
1 0 1 1 0 1
0 1 0 0 1 0
original binary number
Bù 1 (complement each bit to form 1’s complement)
Bù 2 (2’s-Complement )Form
binary equivalent of 45 10
complement each bit to form 1’s complement
1 0 1 1 0 1
0 1 0 0 1 0
0 0 0 0 0 1
0 1 0 0 1 1
+
add 1 to form 2’s complement 2’s complement (-45 10 ) of original binary number
Trang 5HCMC University of Technology and Education
Faculty of Electrical & Electronic Engineering Addition in 2’s-Complement System
Trang 6Faculty of Electrical & Electronic Engineering
Assoc Prof Nguyen Thanh Hai, PhD
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Số trừ trong hệ thống bù 2
01001 (+9 10 )
11100 (-4 10 )
1 00101 (+5 10 ) +
Disregard, result: 00101 = +5 10
Example 5.3
2’s-Complement Form
0 0 1 0 0 (nhị phân gốc, +4)
1 1 0 1 1 (bù 1)
0 0 0 0 1
1 1 1 0 0 (bù 2 của +4 là -4
+
Trang 7HCMC University of Technology and Education
Faculty of Electrical & Electronic Engineering
11100 (-4 10 ) bù 2 của 4
10111 (-9 10 ) bù 2 của 9
1 10011 (-13 10 )
+
Disregard
11100 (-4 10 ) bù 2 của 4
01001 (+9 10 )
-Example 5.4
- complement each bit (+9) to form
1’s complement=10110
- add 1 to form 2’s complement and
- Use 2’s complement for 01001 (+9 10 )
Result:
Số trừ nhị phân trong hệ thống bù 2
11100 (-4 10 )
- 01001 (-9 10 ) +
10011 (-13 10 )
01100 Bù 1
00001 (cộng)
01101 (+13)
Trang 8Faculty of Electrical & Electronic Engineering
Assoc Prof Nguyen Thanh Hai, PhD
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Cộng 2 số BCD
Tổng nhỏ hơn hay bằng 9 (Sum Equals 9 or less) Example 5
Example 6
Trang 9HCMC University of Technology and Education
Faculty of Electrical & Electronic Engineering
Example 9.7
Example 9.8
Always + 6, meaning 9 (BCD)+6=15, 4 bits can count from 0-15 Tổng lớn hơn 9 (Sum Greater than 9)
Trang 10Faculty of Electrical & Electronic Engineering
Assoc Prof Nguyen Thanh Hai, PhD
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Sum Greater than 9
Example 9
Example 10
Tổng lớn hơn 9 (Sum Greater than 9)
Trang 11HCMC University of Technology and Education
Faculty of Electrical & Electronic Engineering
The End