Digital Logic Toolkit

Digital Logic Toolkit — Multiplexers & decoders

Source
https://digitallogictoolkit.com/multiplexers-decoders/
Printed

2:4 decoder, A₁A₀ = 11 — multiplexers and decoders

coreone-hot output

Answer

Y0 = 0, Y1 = 0, Y2 = 0, Y3 = 1

Why this example is worth doing

A decoder asserts exactly one output, chosen by its input as a binary number — the one-hot encoding. The page points out that each output is a single minterm of the input variables, so a decoder is literally a minterm generator, and that is the key to the next example. It also connects back to the three-state bus: a decoder is how you guarantee exactly one driver is enabled.

Try your own input in the Multiplexers & decoders. Multiplexers from 2:1 to 16:1 and decoders from 2:4 to 4:16, with the selection logic derived.

How the answer is reached

The probed row

A1 = 1, A0 = 1

Output table

Output table — columns A1, A0, Y0, Y1, Y2, Y3
A1A0Y0Y1Y2Y3
001000
010100
100010
110001

Compare with

Open the Multiplexers & decoders

This input is entered in the tool itself — it is too rich for a link to carry.

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