P7.27. Write a Boolean expression for the output of each of the logic circuits shown in Figure P7.270. Figure P7.27 B
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- Consider the circuit shown in Figure P7.35. The switches are controlled by logic variables such that, if A is high, switch A is closed, and if A is low, switch A is open. Conversely, if B is high, the switch labeled B ¯ is open, and if B is low, the switch labeled B ¯ is closed. The output variable is high if the output voltage is 5 V, and the output variable is low if the output voltage is zero. Write a logic expression for the output variable. Construct the truth table for the circuit.P7.27. Write a Boolean expression for the output of each of the logic circuits shown in Figure P7.270. Figure P7.27 BD A ВSuppose we need a logic circuit with a logic output G that is high only if a certain hexadecimal digit is 1, 5, B, or F. The inputs to the logic circuit are the bits B 8 , B 4 , B 2 and B 1 of the binary equivalent for the hexadecimal digit. (The MSB is B 8 and the LSB is B 1 ) a. Fill in the Karnaugh map shown in Figure T7.6. b. Determine the minimized SOP expression for G. c. Determine the minimum POS expression for G.
- Write a Boolean expression for the output of each of the logic circuits shown in Figure P7.27.For the logic circuit of Figure T7.5: a. write the logic expression for D in terms of A, B, and C directly from the logic diagram; b. construct the truth table and the Karnaugh map; c. determine the minimum SOP expression for D; d. determine the minimum POS expression for D.Consider Table P7.40. A, B, and C represent logic-variable input signals; F through K are outputs. Using the product-of-sums approach, write a Boolean expression for F in terms of the inputs. Repeat by using the sum-of-products approach. Repeat Problem P7.40 for K.
- Consider Table P7.40. A, B, and C represent logic-variable input signals; F through K are outputs. Using the product-of-sums approach, write a Boolean expression for F in terms of the inputs. Repeat by using the sum-of-products approach. Repeat Problem P7.40 for I.Consider Table P7.40. A, B, and C represent logic-variable input signals; F through K are outputs. Using the product-of-sums approach, write a Boolean expression for F in terms of the inputs. Repeat by using the sum-of-products approach.Consider Table P7.58 in which A, B, C, and D are input variables. F, G, H, and I are the output variables. a. Construct a Karnaugh map for the output variable F. b. Find the minimum SOP expression for this logic function. c. Use AND, OR, and NOT gates to realize the minimum SOP function. d. Find the minimum POS expression. Repeat Problem P7.58 for output variable I.
- Palagiaph 1. Find logic finctions for the circuits shown below. FFigure P7.87 shows the functional diagram of an electronic die that can be used in games of chance. The system contains a high-speed clock, a push-button momentary contact switch that returns to the upper (logic 1) position when released, and a counter that counts through the cycle of states: 001, 010, 011, 100, 101, 110 (i.e., the binary equivalents of the number of spots on the various sides of the die). Q 3 is the MSB, and Q 1 is the LSB. The system has a display consisting of seven light-emitting diodes (LED), each of which lights when logic 1 is applied to it. The encoder is a combinatorial logic circuit that translates the state of the counter into the logic signals needed by the display. Each time the switch is depressed, the counter operates, stopping in a random state when the switch is released. a. Use JK flip-flops having asynchronous preset and clear inputs to draw the detailed diagram of the counter. b. Design the encoder, using Karnaugh maps to minimize the logic elements…Assuming that the initial state of the shift register shown in Figure P7.81 is 100 (i.e., Q 0 =1, Q 1 =0, and Q 2 = 0), find the successive states. After how many shifts does the register return to the starting state?