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

coreone low input forces the output high

Answer

output 1

Why this example is worth doing

With one input low the AND is 0 and the NAND is therefore 1. Generalised: a NAND is low only when every input is high, at any width. The page notes that three- and four-input NANDs are common physical parts while eight-input ones are rare, because stacking that many transistors in series degrades the drive strength — a rare place where the electrical reality visibly constrains the logic design.

Try your own input in the NAND gate. Truth table, symbol and algebraic form for (A·B)′, the universal gate.

How the answer is reached

The probed row

A = 1, B = 1, C = 01Row 6 of 8.

Truth table

Truth table — columns #, A, B, C, A ↑ B ↑ C
#ABCA ↑ B ↑ C
00001
10010
20101
30110
41001
51010
61101
71111

Compare with

Open this example in the NAND 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
  • Sheffer, “A Set of Five Independent Postulates for Boolean Algebras” (1913)