Sum of Products

Sum of Products (SOP) Form

Any Boolean function can be expressed as a Sum of Products (SOP) — an OR of AND terms.

Each AND term is called a minterm. A minterm corresponds to a row in the truth table where the output is 1. It's the product (AND) of all input variables, where each variable appears either uncomplemented or complemented.

For example, if a 2-input function outputs 1 only at row 10 (A=1, B=0):

• Minterm = A AND NOT(B) = A·B'

The canonical SOP is formed by ORing all minterms.

Finding Minterms

Given the truth table output array [0, 0, 1, 1] for inputs ordered 00, 01, 10, 11:

• Row 0 (00) → 0 (not a minterm)
• Row 1 (01) → 0 (not a minterm)
• Row 2 (10) → 1 → minterm 2
• Row 3 (11) → 1 → minterm 3

Minterms: [2, 3]

Your Task

Implement minterms(outputs) that takes an array of truth-table outputs (length must be a power of 2) and returns an array of minterm indices (rows where output is 1).

Then implement evalSOP(minterms, n, inputs) that evaluates a function at given inputs using its minterm list: return 1 if the input combination index is in minterms, else 0.