Q.(a) What are logic gates?

The AND Gate: The "All-or-Nothing" Gate

Imagine you are trying to start a car. Two things must happen: you must turn the key, and you must press the brake pedal. If either one is missing — you turn the key without pressing the brake, or you press the brake without the key — the engine stays off. Only when both actions happen together does the car start.

That is exactly what an AND gate does. It is the "all-or-nothing" gate: the output is 1 only when every single input is 1. If even one input is 0, the output is 0.

The Precise Statement

An AND gate takes two (or more) binary inputs — each either 0 (false, off) or 1 (true, on) — and produces one binary output. The rule is:

The dot ($\cdot$) is the Boolean multiplication symbol. It does not mean ordinary arithmetic multiplication; it means logical AND. The output $Y$ is 1 if and only if $A = 1$ and $B = 1$.

Truth Table (for two inputs)

Only the last row — both inputs high — gives a high output.

Why "Multiplication"?

The name "AND" comes from everyday language: "I will go to the park if it is sunny and I have free time." Both conditions must be true. The symbol $\cdot$ (dot) is used because, in Boolean algebra, AND behaves like multiplication in ordinary arithmetic when you only use 0 and 1:

• $0 \times 0 = 0$
• $0 \times 1 = 0$
• $1 \times 0 = 0$
• $1 \times 1 = 1$

So $A \cdot B$ literally gives the same result as multiplying the two bits. That is why the AND gate is also called a product gate.

More Than Two Inputs

An AND gate can have three, four, or more inputs. The rule stays the same: output is 1 only when every input is 1. For a 3-input AND gate:

Truth table (abbreviated):

Only the very last combination — all three inputs 1 — lights up the output.

Real-World Analogy …