Questions: Combinational Circuit Design

Question 1

A combinational circuit outputs 1 when exactly two of three inputs (A, B, C) are 1. How many minterms appear in its canonical sum-of-products expression?

• A. 2
• B. 3
• C. 4
• D. 6

Answer: (B)

Exactly-two-of-three is true for input combinations 011, 101, and 110 — three minterms (m3, m5, m6). Each minterm is a row of the truth table where the output is 1. Writing the canonical SOP means summing those three product terms: (NOT A AND B AND C) + (A AND NOT B AND C) + (A AND B AND NOT C).

Question 2

A combinational circuit's output can depend on what the inputs were one clock cycle ago.

• T. True
• F. False

Answer: False

By definition, a combinational circuit has no memory — its output is a pure function of its current inputs with no stored state. Circuits that can remember previous inputs are sequential circuits, which add flip-flops or latches to hold state. This is the fundamental distinction between combinational and sequential logic.

Question 3

What is the purpose of grouping cells in a Karnaugh map, and what rule governs which cells can be grouped?

Model answer: Grouping adjacent 1-cells in a K-map identifies minterms that share all variables except one (or more), so those variables cancel out and simplify the product term. Groups must be powers of 2 in size (1, 2, 4, 8...) and must be rectangular — this corresponds algebraically to applying the absorption or combining law to eliminate variables.

When two minterms differ in exactly one variable (e.g., ABC and AB'C), that variable can be dropped (A·B·C + A·B'·C = A·C). K-maps arrange minterms so that adjacent cells differ in exactly one variable, making the cancellation visually obvious. Larger groups eliminate more variables, producing simpler terms — which is why you always seek the largest valid groups.