Lecture 13 Problems Mano Problems Mano Obtain the

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) 2

Problems (Mano) 3

Problem (Mano) Design a combinational circuit with three inputs and one output a) b) 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 4

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

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

Example: Three 1 s Detector ° Problem: Detect three consecutive 1 s in 8 -bit input: abcdefgh - 00011101 1 11110000 1 10101011 0 • 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 1 s y = abc + bcd + cde + def + efg + fgh • Step 2: Convert to equation -- already done • Step 3: Implement as a gate-based circuit °a °b °c °abc °bcd °d °cde °e °y °def °f °g °efg °fgh °h 20

Example: Number of 1 s Count ° Problem: Output in binary on two outputs yz the number of 1 s 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 °a °b • Step 3: Implement as a gate-based °c circuit °a °b °c °a °b °y °c °a °b °c °z °a °b °c 21