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# Lecture 13 Problems (Mano)

Lecture 13 Problems (Mano). Problems (Mano). Obtain the simplified Boolean expressions for outputs F and G in terms of the input variables in (A,B,C and D). Problems (Mano). Problem (Mano). Design a combinational circuit with three inputs and one output

## Lecture 13 Problems (Mano)

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1. Lecture 13Problems (Mano)

2. 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. Problems (Mano)

4. Problem (Mano) Design a combinational circuit with three inputs and one output • The output is 1 when binary value of the inputs is less than 3, the output is zero otherwise • The output is 1 when binary value of the inputs is an odd number

5. Problem (Mano) Design a combinational circuit with three inputs and one output • The output is 1 when binary value of the inputs is an odd number

6. Problem (Mano) 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

7. Problem (Mano) 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

8. Problem (Mano) 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

9. Problem (Mano) 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

10. Problem (Mano) 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

11. Problem (Mano) 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

12. Problem (Mano) 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

13. Problem (Mano) 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

14. Problem (Mano) 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

15. Problem (Mano) 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

16. Problem (Mano) Design a combinational circuit that converts a four bit Gray code to four bit binary number

17. Problem (Mano) Design a combinational circuit that converts a four bit Gray code to four bit binary number

18. Problem (Mano) Design a combinational circuit that converts a four bit Gray code to four bit binary number

19. Problem (Mano) Design a combinational circuit that converts a four bit Gray code to four bit binary number

20. a • abc • b • c • bcd • d • cde • e • y • def • f • efg • g • fgh • h Example: Three 1s Detector • 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 done • Step 3: Implement as a gate-based circuit

21. a • b • c • a • b • c • a • b • c • a • y • z • b • c • a • b • c • a • b • a • b • c Example: Number of 1s Count • Problem: Output in binary on two outputs yz the number of 1s on three inputs • 010  01 101  10 000  00 • Step 1: Capture the function • Truth table or equation? • 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 circuit

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