please answer #3 in entirety. ALL PARTS 3. The exclusive NOR (XNOR) function can be expressed as follows:(a + b)' = XNOR(a, b) = Σm(0, 3)(a) Write the canonical SOP and POS expressions for the function.(b) Draw logic diagrams using AND, OR and NOT gates that represent the SOP andPOS expressions.(c) Assuming that the cost of a gate is 1+ number of gate inputs (same as what wasdiscussed in class), determine the cost of the SOP and POS logic diagrams inpart 3b. You must explain your answer by showing the cost of each gate in yourcircuit and the total cost.(d) Use Boolean algebra to show that the canonical SOP and POS expressions areequal. (e) Draw a logic diagram that implement the XNOR function using only NANDgates. You must explain you placement of bubbles and any additional gates.(f) Draw a logic diagram that implements the XNOR function using only NORgates. Again you must explain you placement of bubbles and any additionalgates.(g) Use Boolean algebra to show that your logic diagrams in parts 3e and 3f producethe POS or SOP expressions in part 3a. Here you must start with (xy)' for eachNAND gate with inputs x, y. Similarly, you must start with (x+y)' for each NORgate with inputs x, y.

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3. The exclusive NOR (XNOR) function can be expressed as follows: (a + b)' = XNOR(a, b) = Σm(0, 3) (a) Write the canonical SOP and POS expressions for the function. (b) Draw logic diagrams using AND, OR and NOT gates that represent the SOP and POS expressions. (c) Assuming that the cost of a gate is 1+ number of gate inputs (same as what was discussed in class), determine the cost of the SOP and POS logic diagrams in part 3b You must explain your answer by showing the cost of each gate in your circuit and the total cost.

3. The exclusive NOR (XNOR) function can be expressed as follows: (a + b)' = XNOR(a, b) = Σm(0, 3) (a) Write the canonical SOP and POS expressions for the function. (b) Draw logic diagrams using AND, OR and NOT gates that represent the SOP and POS expressions. (c) Assuming that the cost of a gate is 1+ number of gate inputs (same as what was discussed in class), determine the cost of the SOP and POS logic diagrams in part 3b You must explain your answer by showing the cost of each gate in your circuit and the total cost.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

please answer #3 in entirety. ALL PARTS

3. The exclusive NOR (XNOR) function can be expressed as follows:
(a + b)' = XNOR(a, b) = Σm(0, 3)
(a) Write the canonical SOP and POS expressions for the function.
(b) Draw logic diagrams using AND, OR and NOT gates that represent the SOP and
POS expressions.
(c) Assuming that the cost of a gate is 1+ number of gate inputs (same as what was
discussed in class), determine the cost of the SOP and POS logic diagrams in
part 3b. You must explain your answer by showing the cost of each gate in your
circuit and the total cost.
(d) Use Boolean algebra to show that the canonical SOP and POS expressions are
equal.

(e) Draw a logic diagram that implement the XNOR function using only NAND
gates. You must explain you placement of bubbles and any additional gates.
(f) Draw a logic diagram that implements the XNOR function using only NOR
gates. Again you must explain you placement of bubbles and any additional
gates.
(g) Use Boolean algebra to show that your logic diagrams in parts 3e and 3f produce
the POS or SOP expressions in part 3a. Here you must start with (xy)' for each
NAND gate with inputs x, y. Similarly, you must start with (x+y)' for each NOR
gate with inputs x, y.

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