A ⊕ B ⊕ C — logic gate diagram

core2 XOR gates chained

Answer

1 gates, 3 inputs; output column 01101001

Why this example is worth doing

A three-input XOR drawn as a chain of two two-input gates, because three-input XOR is not a standard physical part. This is the first diagram whose structure is a choice rather than a transcription: the same function can be drawn as a chain, which is cheap and has two gate delays, or as a balanced tree, which matters once there are eight inputs. The page shows both and gives the depth formula, connecting the drawing to the propagation-delay question that follows it in most courses.

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
g0xori0, i1, i2

Truth table

Truth table — columns #, A, B, C, F
#ABCF
00000
10011
20101
30110
41001
51010
61100
71111

Compare with

Open this example in the Logic gate diagram builder

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