Minimisation and Canonical Forms

Minimisation & Canonical Forms

A simpler boolean expression means a cheaper, faster circuit with fewer gates, less delay, and less power. Minimisation is finding an equivalent expression with as few terms and literals as possible.

Two canonical forms name functions unambiguously:

Canonical forms provide a clear starting point, but they are rarely minimal.

Simplifying Logic & Pitfalls

Two primary tools perform logic simplification:

• Boolean algebra: Applies identities directly. Example: $AB + A\overline{B} = A(B + \overline{B}) = A$, collapsing two terms because $B$ is redundant.
• Karnaugh map (K-map): A visual grid where adjacent cells differ in one variable. Circle groups of 1s in powers of two ($1, 2, 4, 8$) to eliminate variables.

Common Pitfall: Circling group sizes that are not a power of two, or missing the wrap-around adjacency where left/right and top/bottom edges are neighbors. Both errors yield non-minimal or incorrect circuits.