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1- For the Boolean function: F = xy'z + x'y'z + w'xy + wx'y + wxy (a) Obtain the truth table of F. (b) Draw the logic diagram, using the original Boolean expression. (c) Use Boolean algebra to simplify the function to a minimum number of literals.

1- For the Boolean function: F = xy'z + x'y'z + w'xy + wx'y + wxy (a) Obtain the truth table of F. (b) Draw the logic diagram, using the original Boolean expression. (c) Use Boolean algebra to simplify the function to a minimum number of literals.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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1- For the Boolean function: F = xy'z + x'y'z + w'xy + wx'y + wxy (a) Obtain the truth table of F. (b) Draw the logic diagram, using the original Boolean expression. (c) Use Boolean algebra to simplify the function to a minimum number of literals. (d) Obtain the truth table of the function from the simplified expression and show that it is the same as the one in part (a). (e) Draw the logic diagram from the simplified expression and compare the total number of gates with the diagram of part (b). 2- Obtain the truth table of the following functions and express each function in sum of minterms. a) (xy + z) (y + xz) b) (A' + B) (B'+C) c) y'z+ wxy' +wxz' +w'x' z 3- Find a minimal Boolean equation for the function expressed by the following truth table. Remember to take advantage of the don't care entries. Sketch a circuit for the function. A B D Y X 1 X 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 X 1 4- Implement the following four Boolean expressions with three half adders: D=ΑΘΒ C E = A' BC + AB'C F = ABC' + (A' + B')C G = ABC 5- Derive the circuits for a three-bit parity generator and four-bit parity checker using an odd parity bit. 6- Design a combinational circuit with three inputs and one output. (a)The output is 1 when the binary value of the inputs is less than 3. The output is 0 otherwise. (b) The output is 1 when the binary value of the inputs is an even number. 이0101 0101 0 1o
Transcribed Image Text:1- For the Boolean function: F = xy'z + x'y'z + w'xy + wx'y + wxy (a) Obtain the truth table of F. (b) Draw the logic diagram, using the original Boolean expression. (c) Use Boolean algebra to simplify the function to a minimum number of literals. (d) Obtain the truth table of the function from the simplified expression and show that it is the same as the one in part (a). (e) Draw the logic diagram from the simplified expression and compare the total number of gates with the diagram of part (b). 2- Obtain the truth table of the following functions and express each function in sum of minterms. a) (xy + z) (y + xz) b) (A' + B) (B'+C) c) y'z+ wxy' +wxz' +w'x' z 3- Find a minimal Boolean equation for the function expressed by the following truth table. Remember to take advantage of the don't care entries. Sketch a circuit for the function. A B D Y X 1 X 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 X 1 4- Implement the following four Boolean expressions with three half adders: D=ΑΘΒ C E = A' BC + AB'C F = ABC' + (A' + B')C G = ABC 5- Derive the circuits for a three-bit parity generator and four-bit parity checker using an odd parity bit. 6- Design a combinational circuit with three inputs and one output. (a)The output is 1 when the binary value of the inputs is less than 3. The output is 0 otherwise. (b) The output is 1 when the binary value of the inputs is an even number. 이0101 0101 0 1o
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