Boolean constant

Also called: Boolean constants, constants, logic constant, constant 0, constant 1

One of the two fixed values in Boolean algebra, 0 (false, low) and 1 (true, high). In a circuit, a wire tied permanently low or high.

Boolean algebra has exactly two constants: 0 (false) and 1 (true). In a circuit, 0 is a wire tied to ground (low voltage) and 1 is a wire tied to the supply (high voltage).

Constants appear in the laws, and they are often the key to simplifying:

With OR: = A (identity) and = 1 (null).
With AND: = A (identity) and = 0 (null).
From complements: = 1 and = 0 (complement law).
Flipping: = 1 and = 0.

When forming a dual, 0 and 1 swap along with AND and OR.

In practice, constants turn up mid-simplification, after the complement law turns something into 0 or 1. The next step is almost always identity or null to make them disappear.

Worked examples

Example

Evaluating with constants

What is the value of ?

1.
NOT first: = 0.
2.
Then AND: 1 · 0 = 0.
3.
Then OR: 0 + 0 = 0.
4.
Result: 0.

Example

The dual of an expression with constants

Find the dual of .

1.
Swap · with +, and 0 with 1.
2.
becomes , and the + 1 becomes · 0.
3.
Dual: .
4.
The original simplifies to 1 and the dual to 0: duals of constants swap 0 and 1.

Common mistakes

Forgetting to swap 0 and 1 when forming a dual.
Treating 1 + 1 as 2. Constants stay 0 or 1.

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Boolean Algebra lesson

Practice exams

Boolean Algebra: Exam 3 · 1 question

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Boolean constant is taught in Boolean Algebra.

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