Digital Logic Design - Lecture 13: Problems (Mano)

Lecture 13Problems (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 outputThe output is 1 when binary value of the inputs is less than 3, the output is zero otherwiseThe output is 1 when binary value of the inputs is an odd numberProblem (Mano)Design a combinational circuit with three inputs and one outputThe output is 1 when binary value of the inputs is an odd numberProblem (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 inputProblem (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 inputProblem (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 inputProblem (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 gatesProblem (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 gatesProblem (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 gatesProblem (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 gatesProblem (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 gatesProblem (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 gatesProblem (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 gatesProblem (Mano)Design a combinational circuit that converts a four bit Gray code to four bit binary numberDesign a combinational circuit that converts a four bit Gray code to four bit binary numberProblem (Mano)Design a combinational circuit that converts a four bit Gray code to four bit binary numberProblem (Mano)Design a combinational circuit that converts a four bit Gray code to four bit binary numberProblem (Mano)Example: Three 1s DetectorProblem: Detect three consecutive 1s in 8-bit input: abcdefgh00011101  1 10101011  0 11110000  1Step 1: Capture the functionTruth table or equation? Truth table too big: 28 = 256 rowsEquation: create terms for each possible case of three consecutive 1sy = abc + bcd + cde + def + efg + fghStep 2: Convert to equation -- already doneStep 3: Implement as a gate-based circuitbcddeffghabccdeefgyabcdefghExample: Number of 1s CountProblem: Output in binary on two outputs yz the number of 1s on three inputs010  01 101  10 000  00Step 1: Capture the functionTruth table or equation? Truth table is straightforwardStep 2: Convert to equationy = a’bc + ab’c + abc’ + abcz = a’b’c + a’bc’ + ab’c’ + abcStep 3: Implement as a gate-based circuitabcabcabcabczabcabcaby