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Logic and Truth Tables

Inputs and outputs are 1 or 0. A truth table lists every combination of inputs and the output for each.

True and False as 1 and 0

In logic, a statement is either true or false . We write true as 1 and false as 0 — the same as on and off in a circuit. We give each input a capital letter: A, B, C \dots The output is often called Q or X .

Each input can be 0 or 1. With n inputs there are 2ⁿ combinations, so the truth table has 2ⁿ rows . Inputs Rows 122438416

The safest way is to count in binary, starting from 0. For three inputs A, B and C, count from 000 to 111:

The 8 input combinations for A, B, C
The 8 input combinations for A, B, C

A pattern check: the last column goes 0,1,0,1\dots; the middle goes 0,0,1,1\dots; the first goes 0,0,0,0,1,1,1,1.

Practice

A circuit has 4 inputs. How many rows does its truth table have?

Your answer

True and False as 1 and 0

In logic, a statement is either true or false . We write true as 1 and false as 0 — the same as on and off in a circuit. We give each input a capital letter: A, B, C \dots The output is often called Q or X .

Inputs

Rows

Listing the Rows Without Missing Any

The safest way is to count in binary, starting from 0. For three inputs A, B and C, count from 000 to 111:

The 8 input combinations for A, B, C
The 8 input combinations for A, B, C

A pattern check: the last column goes 0,1,0,1\dots; the middle goes 0,0,1,1\dots; the first goes 0,0,0,0,1,1,1,1.

Practice

A circuit has 4 inputs. How many rows does its truth table have?

Your answer