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3. The exclusive NOR (XNOR) function can be expressed as follows: (a + b)' = XNOR(a, b) = Σm(0, 3)

3. The exclusive NOR (XNOR) function can be expressed as follows: (a + b)' = XNOR(a, b) = Σm(0, 3)

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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please answer part 3e

3. The exclusive NOR (XNOR) function can be expressed as follows: \[ (a \oplus b)' = \text{XNOR}(a, b) = \sum m(0, 3) \] This equation describes the logic function known as the exclusive NOR (XNOR). The expression \((a \oplus b)'\) represents the complement of the exclusive OR (XOR) operation between two variables \(a\) and \(b\). In Boolean algebra, this is equivalent to the XNOR operation, which outputs true only when both inputs are the same. The summation notation \(\sum m(0, 3)\) indicates the minterms for which the XNOR function is true, specifically for the binary inputs 00 and 11. Minterms are the combinations of variables for which the function evaluates to true (or 1) in a truth table.
Transcribed Image Text:3. The exclusive NOR (XNOR) function can be expressed as follows: \[ (a \oplus b)' = \text{XNOR}(a, b) = \sum m(0, 3) \] This equation describes the logic function known as the exclusive NOR (XNOR). The expression \((a \oplus b)'\) represents the complement of the exclusive OR (XOR) operation between two variables \(a\) and \(b\). In Boolean algebra, this is equivalent to the XNOR operation, which outputs true only when both inputs are the same. The summation notation \(\sum m(0, 3)\) indicates the minterms for which the XNOR function is true, specifically for the binary inputs 00 and 11. Minterms are the combinations of variables for which the function evaluates to true (or 1) in a truth table.
(e) Draw a logic diagram that implements the XNOR function using only NAND gates. You must explain your placement of bubbles and any additional gates.
Transcribed Image Text:(e) Draw a logic diagram that implements the XNOR function using only NAND gates. You must explain your placement of bubbles and any additional gates.
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