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Number of 2:1 multiplexers required to design a 256:1 mux

Number of 2:1 multiplexers required to design a 256:1 mux

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Nov 3, 2026

To build a 256:1256{:}1 multiplexer using only 2:12{:}1 multiplexers, you arrange the 256256 data inputs into a binary “mux tree” so that every 2:12{:}1 multiplexer reduces the number of candidates by 11. In general, the number of 2:12{:}1 multiplexers required to implement an N:1N{:}1 multiplexer is N−1N-1. Therefore for N=256N=256:

\text{# of }2{:}1\text{ MUX} = 256 - 1 = 255

So the blank is 255.2

Footnotes

  1. Filo - Number of 2:1 mux requires designing 256:1 mux is..... - States the general formula N−1N-1 for number of 2:12{:}1 MUXes to build N:1N{:}1 and computes 256−1=255256-1=255. ↩

  2. Testbook - Find the number of 2×1 MUX multiplexers required to implement ... - Gives (2n−1)(2^n-1) / (N−1)(N-1) type rule and shows stage-sum reasoning. ↩

How many 2:1 multiplexers are required to design 256:1 mux?

Key ideas behind the count

A 2:12{:}1 multiplexer has two data inputs and one output; in a mux-tree design, each 2:12{:}1 block “merges” two signals into one. After you merge 256256 signals down to 11 signal, you have performed exactly 255255 merges, i.e. you used 255255 2:12{:}1 multiplexers.2

[Keyword]{def="A k:1k{:}1 multiplexer selects 1 of k inputs using select lines"} MuxTree 2to1 InternalNode.

Footnotes

  1. Filo - Number of 2:1 mux requires designing 256:1 mux is..... - States the general formula N−1N-1 for number of 2:12{:}1 MUXes to build N:1N{:}1 and computes 256−1=255256-1=255. ↩

  2. GeeksforGeeks - Multiplexers in Digital Logic - Lists examples: 8:18{:}1 needs 77 2:12{:}1, 16:116{:}1 needs 1515, 64:164{:}1 needs 6363, and concludes the (N−1)(N-1) pattern. ↩

Compute # of 2:1 MUXes for 256:1 (mux-tree)

  1. 1
    Step 1

    For an N:1N{:}1 multiplexer built from 2:12{:}1 multiplexers, the count is N−1N-1.2

    Footnotes

    1. Filo - Number of 2:1 mux requires designing 256:1 mux is..... - States the general formula N−1N-1 for number of 2:12{:}1 MUXes to build N:1N{:}1 and computes 256−1=255256-1=255. ↩

    2. Testbook - Find the number of 2×1 MUX multiplexers required to implement ... - Gives (2n−1)(2^n-1) / (N−1)(N-1) type rule and shows stage-sum reasoning. ↩

  2. 2
    Step 2

    Compute 256−1=255256-1=255.

  3. 3
    Step 3

    Therefore, 255 2:12{:}1 multiplexers are required.

Quick memory shortcut

If the target mux is 2n:12^n{:}1, the number of 2:12{:}1 muxes is 2n−12^n-1 (e.g., 16:116{:}1 needs 1515).

Footnotes

  1. GeeksforGeeks - Multiplexers in Digital Logic - Lists examples: 8:18{:}1 needs 77 2:12{:}1, 16:116{:}1 needs 1515, 64:164{:}1 needs 6363, and concludes the (N−1)(N-1) pattern. ↩

Examples of 2:1 MUX counts using the N−1N-1 rule

Shows the general relationship: N:1N{:}1 mux needs (N−1)(N-1) two-to-one muxes.

Common confusions

Knowledge Check

Question 1 of 3
Q1Single choice

How many 2:1 multiplexers are required to design a 256:1 multiplexer?

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