What is the Boolean expression for the AND gate ?
2025
What is the Boolean expression for the AND gate ?
- A.
A + B
- B.
A . B
- C.
A' + B'
- D.
A' . B'
Attempted by 356 students.
Show answer & explanation
Correct answer: B
Concept
In Boolean algebra the AND operation is logical multiplication: its output is 1 only when every input is 1. It is written with a dot between the variables (A . B), and the dot may even be dropped (AB). Logical addition (the + sign) is a different operation — it denotes OR, whose output is 1 when at least one input is 1.
Applying it here
For two inputs A and B, the AND gate output is therefore A . B (equivalently AB). This is the value that equals 1 only for the input pair where both A and B are 1.
Why the other expressions are different gates
A + B is logical addition, which is the OR gate (output 1 if either input is 1).
A' + B' is the complement of A . B by De Morgan's law, so it is the NAND gate output.
A' . B' is the complement of A + B by De Morgan's law, so it is the NOR gate output.
Cross-check (truth table)
A | B | A . B |
|---|---|---|
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
The output column matches the AND definition: 1 only in the last row where both inputs are 1.