((A·B)′·C)′ — logic gate diagram

core2 NAND gates (4 AND/NOT primitive nodes); bubble cancellation

Answer

4 gates, 3 inputs; output column 10101011

Why this example is worth doing

Two NAND gates in series, which is not the same as an AND followed by a NAND — the bubble on the first output meets the bubble implied at the second input and the two cancel. The page uses this diagram to teach bubble pushing as a visual form of involution and De Morgan: an inversion at an output and an inversion at the input it drives annihilate, so you can slide bubbles along wires freely to make a network's logic readable. It is the single most useful schematic-reading skill in the course.

Try your own input in the Logic gate diagram builder. Draw an expression as a gate schematic in IEEE or IEC symbols and copy it as an image.

How the answer is reached

Netlist

Netlist — columns Node, Gate, Inputs
NodeGateInputs
g0andi0, i1
g1notg0
g2andg1, i2
g3notg2

Truth table

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

Compare with

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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