A·B + C·D — truth table

exam standard16 rows, 7 true

Answer

16 rows, 7 true (3, 7, 11, 12, 13, 14, 15)

Why this example is worth doing

Four variables, sixteen rows, and the first table that will not fit on a phone screen. It is here to demonstrate the mobile behaviour promised in the spec: the table scrolls horizontally inside its own container with the variable columns pinned, while the page itself never scrolls sideways. It is also the canonical two-level AND-OR structure, so the converter bar leads directly to a gate diagram of exactly two AND gates feeding one OR gate.

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, D, A · B + C · D
#ABCDA · B + C · D
000000
100010
200100
300111
401000
501010
601100
701111
810000
910010
1010100
1110111
1211001
1311011
1411101
1511111

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)