Bollean logic

What is an AND gate?

Outputs 1 only when both inputs are 1 — if either input is 0 the output is 0

What is an OR gate?

Outputs 1 when at least one input is 1 — only outputs 0 when both inputs are 0

What is a NOT gate?

Inverts the input — if input is 1 output is 0 — if input is 0 output is 1 — also called a NOT gate or inverter

Complete the truth table for AND

A=0 B=0 → 0. A=0 B=1 → 0. A=1 B=0 → 0. A=1 B=1 → 1

Complete the truth table for OR

A=0 B=0 → 0. A=0 B=1 → 1. A=1 B=0 → 1. A=1 B=1 → 1

Complete the truth table for NOT

A=0 → 1. A=1 → 0

What is the output of A AND B when A=1 and B=0?

0 — because both inputs must be 1 for AND to output 1

What is the output of A OR B when A=0 and B=1?

1 — because at least one input is 1

What is the output of NOT A when A=1?

0 — NOT inverts the input

Complete the truth table for A AND (NOT B)

A=0 B=0 → NOT B=1 → 0 AND 1 = 0. A=0 B=1 → NOT B=0 → 0 AND 0 = 0. A=1 B=0 → NOT B=1 → 1 AND 1 = 1. A=1 B=1 → NOT B=0 → 1 AND 0 = 0

Complete the truth table for (A OR B) AND (NOT A)

A=0 B=0 → 0 AND 1 = 0. A=0 B=1 → 1 AND 1 = 1. A=1 B=0 → 1 AND 0 = 0. A=1 B=1 → 1 AND 0 = 0

How do you work out the output of a logic diagram with multiple gates?

Work from left to right — calculate the output of each gate in order — use the outputs of earlier gates as inputs to later gates — build up a truth table column by column