Truth tables Boolean expressions and K-maps

A truth table is the specification of a combinational function. Write every input combination before simplifying the implementation.

Choose and label a variable order. With inputs A, B, C, minterm numbers normally use A as the most significant bit: 101 is minterm 5. Canonical SOP contains one product term for each row with output 1. A minimal expression implements the same truth table with fewer terms or literals; verify equivalence across all rows.

Use Gray-code order 00, 01, 11, 10 on a two-bit K-map axis. Groups contain powers of two cells and may wrap across boundaries. Diagonal cells alone are not adjacent. Mark a don’t-care only when that input is genuinely unspecified, not merely inconvenient.

De Morgan’s laws are NOT(A AND B) = NOT A OR NOT B and NOT(A OR B) = NOT A AND NOT B. NAND-only implementations can use NAND(A,A) as an inverter. Gate count and delay depend on the actual implementation, including complemented inputs and allowed fan-in.

For arithmetic truth tables, interpret signed input before evaluating the mathematical expression, then encode the output at its declared width. Check range/overflow explicitly.