Lecture Digital logic design - Lecture 13: Problems (Mano)

Lecture Digital logic design - Lecture 13: Problems (Mano). The main contents of the chapter consist of the following: Design a combinational circuit with three inputs and one output, design a combinational circuit that converts a four bit Gray code to four bit binary number,...

Problems (Mano)

°Obtain the simplified Boolean expressions for outputs F and

G in terms of the input variables in (A,B,C and D)

3

Design a combinational circuit with three inputs x, y and z

and three outputs A, B and C, when the binary input is 0, 1, 2

or 3, the binary output is two greater than the input When the binary input is 4, 5, 6 or 7, the binary output is three less than the input

Design a combinational circuit with three inputs x, y and z

and three outputs A, B and C, when the binary input is 0, 1, 2

or 3, the binary output is two greater than the input When the binary input is 4, 5, 6 or 7, the binary output is three less than the input

Design a combinational circuit with three inputs x, y and z

and three outputs A, B and C, when the binary input is 0, 1, 2

or 3, the binary output is two greater than the input When the binary input is 4, 5, 6 or 7, the binary output is three less than the input

An ABCD-to-seven segment decoder is a combinational circuit that converts a

decimal digit in BCD to an appropriate code for the selection of segments in an

indicator used to display the decimal digit in a familiar form The seven outputs of

the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as

shown in Fig The numeric display chosen to represent the decimal digit is also

shown in Fig Using the truth table and K-Map, design the BCD-to-seven-segment

decoder using the minimum number of gates

An ABCD-to-seven segment decoder is a combinational circuit that converts a

decimal digit in BCD to an appropriate code for the selection of segments in an

indicator used to display the decimal digit in a familiar form The seven outputs of

the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as

shown in Fig The numeric display chosen to represent the decimal digit is also

shown in Fig Using the truth table and K-Map, design the BCD-to-seven-segment

decoder using the minimum number of gates

An ABCD-to-seven segment decoder is a combinational circuit that converts a

decimal digit in BCD to an appropriate code for the selection of segments in an

indicator used to display the decimal digit in a familiar form The seven outputs of

the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as

shown in Fig The numeric display chosen to represent the decimal digit is also

shown in Fig Using the truth table and K-Map, design the BCD-to-seven-segment

decoder using the minimum number of gates

An ABCD-to-seven segment decoder is a combinational circuit that converts a

decimal digit in BCD to an appropriate code for the selection of segments in an

indicator used to display the decimal digit in a familiar form The seven outputs of

the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as

shown in Fig The numeric display chosen to represent the decimal digit is also

shown in Fig Using the truth table and K-Map, design the BCD-to-seven-segment

decoder using the minimum number of gates

An ABCD-to-seven segment decoder is a combinational circuit that converts a

decimal digit in BCD to an appropriate code for the selection of segments in an

indicator used to display the decimal digit in a familiar form The seven outputs of

the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as

shown in Fig The numeric display chosen to represent the decimal digit is also

shown in Fig Using the truth table and K-Map, design the BCD-to-seven-segment

decoder using the minimum number of gates

An ABCD-to-seven segment decoder is a combinational circuit that converts a

decimal digit in BCD to an appropriate code for the selection of segments in an

indicator used to display the decimal digit in a familiar form The seven outputs of

the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as

shown in Fig The numeric display chosen to represent the decimal digit is also

shown in Fig Using the truth table and K-Map, design the BCD-to-seven-segment

decoder using the minimum number of gates

An ABCD-to-seven segment decoder is a combinational circuit that converts a

decimal digit in BCD to an appropriate code for the selection of segments in an

indicator used to display the decimal digit in a familiar form The seven outputs of

the decoder (a, b, c, d, e, f, g) select the corresponding segment in the display as

shown in Fig The numeric display chosen to represent the decimal digit is also

shown in Fig Using the truth table and K-Map, design the BCD-to-seven-segment

decoder using the minimum number of gates

Design a combinational circuit that converts a four bit Gray code to four bit binary number

Design a combinational circuit that converts a four bit Gray code to four bit binary number

Design a combinational circuit that converts a four bit Gray code to four bit binary number

Design a combinational circuit that converts a four bit Gray code to four bit binary number

° Problem: Detect three consecutive 1s

in 8-bit input: abcdefgh

- 00011101  1 10101011  0

11110000  1

• Step 1: Capture the function

- Truth table or equation?

– Truth table too big: 28  = 256 rows – Equation: create terms for each possible  case of three consecutive 1s

- y = abc + bcd + cde + def + efg + fgh

• Step 2: Convert to equation already

° Problem: Output in binary on

two outputs yz the number of

1s on three inputs

• Step 1: Capture the function

– Truth table is straightforward

• Step 2: Convert to equation

- y = a’bc + ab’c + abc’ + abc

- z = a’b’c + a’bc’ + ab’c’ + abc

• Step 3: Implement as a gate-based