Exclusive-OR binary operation can be represented as
[amp_mcq option1=”$\bar{A} \cdot B + A \cdot \bar{B}$” option2=”$A \cdot \bar{B} + \bar{A} \cdot B$” option3=”$A \cdot B + \bar{A} \cdot \bar{B}$” option4=”$(\bar{A} + \bar{B}) \cdot (A + B)$” correct=”option1″]
This question was previously asked in
UPSC CISF-AC-EXE – 2020
A | B | A XOR B
–|—|——–
0 | 0 | 0
0 | 1 | 1
1 | 0 | 1
1 | 1 | 0
The Sum of Products (SOP) representation for this function includes minterms where the output is 1. These are when (A=0 and B=1) or (A=1 and B=0).
– A=0 and B=1 is represented as $\bar{A} \cdot B$.
– A=1 and B=0 is represented as $A \cdot \bar{B}$.
Combining these with an OR operator gives the SOP form: $\bar{A} \cdot B + A \cdot \bar{B}$.
Option A is $\bar{A} \cdot B + A \cdot \bar{B}$, which directly matches the standard SOP form of XOR.
– The standard SOP form of XOR(A, B) is $\bar{A}B + A\bar{B}$.
– Boolean algebra allows representing logic functions using AND (`.`), OR (`+`), and NOT (`bar` or prime).