3-input AND, A = 1, B = 1, C = 0 — AND gate

coreone low input dominates

Answer

output 0

Why this example is worth doing

Three inputs, one of them low, output 0. The generalisation is that AND has an absorbing input value: a single 0 anywhere forces the output regardless of everything else, which is why AND gates are used as gating and blanking elements. The page contrasts this with OR, whose absorbing value is 1, and notes that the absorbing value is exactly the annulment law from the Boolean laws reference showing up as a physical property.

Try your own input in the AND gate. Truth table, symbol and algebraic form for A·B, with a live two-input toggle.

How the answer is reached

The probed row

A = 1, B = 1, C = 00Row 6 of 8.

Truth table

Truth table — columns #, A, B, C, A · B · C
#ABCA · B · C
00000
10010
20100
30110
41000
51010
61100
71111

Compare with

Open this example in the AND gate

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.
  • Gate symbols follow whichever standard the header toggle is set to: ANSI/IEEE Std 91-1984 distinctive shapes, or IEC 60617-12 rectangles.

Sources

  • ANSI/IEEE Std 91-1984, Graphic Symbols for Logic Functions
  • IEC 60617-12, Graphical Symbols for Diagrams — Binary Logic Elements