Tags: #◇Computer Science #◇CSARCH1 #◇Computer Architecture #◇Combinational Circuits #◇Combinational Circuit - Multiplexer

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Combinational Circuit - Multiplexer

◇Overview

This sub-module discusses how to implement combinational circuits using multiplexers.
Objective: Learn how to implement combinational circuits using multiplexers.

◇Definitions

Multiplexers:

• Selects binary information from one of many input lines and directs it to a single output line.
• Also called a data selector.
• Selection is controlled by a set of selection lines.
• Typically has $2^n$ input lines and $n$ selection lines.

Examples of Multiplexers

• Two-to-one-line multiplexer (2x1):
  • $S$ = selection line
  • $I_0, I_1$ = data lines
• Four-to-one-line multiplexer (4x1):
  • $S_1, S_0$ = selection lines
  • $I_0, I_1, I_2, I_3$ = data lines

◇Boolean Function Implementation Using Multiplexer

To implement a Boolean function using a multiplexer:

1. List the inputs of the multiplexer. Under the list, align all the minterms in two rows.
2. The first row lists all those minterms where the chosen variable is complemented, and the second row lists all the minterms with the variable uncomplemented.
3. Circle all minterms of the given function and inspect each column separately.
4. Rules for mapping to inputs:
   • If two minterms in a column are not circled, apply 0 to the corresponding multiplexer input.
   • If two minterms are circled, apply 1 to the corresponding multiplexer input.
   • If the bottom minterm is circled and the top is not circled, apply the variable to the corresponding multiplexer input.
   • If the top minterm is circled and the bottom is not circled, apply the complemented variable to the corresponding multiplexer input.

◇References & Navigation

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