A·B + C — truth table

intro8 rows over A, B, C

Answer

8 rows, 5 true (1, 3, 5, 6, 7)

Why this example is worth doing

The default example, and the one that establishes how the table is laid out: variables in alphabetical order, A as the most significant bit, rows counting up in binary from 000 so that the row index is the minterm number. That convention is not universal — some textbooks count down, and some put the last variable first — so the page states it explicitly and offers a column-order control. The table also carries an intermediate column for A·B, because the marks in an exam are usually for the intermediate columns.

Try your own input in the Truth table generator. Turn an expression into a full truth table, with a column for every sub-expression.

How the answer is reached

Truth table

Truth table — columns #, A, B, C, A · B + C
#ABCA · B + C
00000
10011
20100
30111
41000
51011
61101
71111

Compare with

Open this example in the Truth table generator

The field arrives filled in with this example’s input.

Note:

Notation this page assumes

  • Symbols: · is AND, + is OR, ⊕ is XOR, a prime or an overline is NOT. The field also takes ∧ ∨ ¬ ~ ! & | and the words.
  • Operator precedence, tightest first: NOT, then AND (including juxtaposition), then XOR/XNOR, then NAND/NOR, then OR, then IMPLIES, then IFF.
  • In a minterm index the first variable is the most significant bit, so over [A, B, C] minterm 5 is A·B̄·C.

Sources

  • Boole, An Investigation of the Laws of Thought (1854)
  • Shannon, “A Symbolic Analysis of Relay and Switching Circuits” (1938)