Priority Encoder & Multiplexer: Operation, Implementation & Boolean Function, Slides of Digital Logic Design and Programming

Download Priority Encoder & Multiplexer: Operation, Implementation & Boolean Function and more Slides Digital Logic Design and Programming in PDF only on Docsity!

Priority Encoder

Multiplexer

Priority Encoder

• (^) The operation of the priority encoder is

such that if two or more inputs are equal to

1 at the same time, the input having the

highest priority will take precedence.

4-input Priority Encoder

Priority Encoder

Multiplexer

V.Saritha@VIT University

4 – to – 1 line multiplexer

Multiplexers

• (^) In general, a 2n^ – to – 1 line multiplexer is

constructed from an n – to – 2n^ decoder by

adding to it 2

n

input lines, one to each

AND gate.

• (^) The outputs of the AND gates are applied

to a single OR gate to provide the 1-line

output.

V.Saritha@VIT University Quadruple 2 – to – 1 line Multiplexers

Boolean Function Implementation

• (^) The min terms out of the decoder to be chosen can be controlled with the input lines.
• (^) The minterms to be included with the function are chosen by making their corresponding input lines equal to 1
• (^) Those minterms not included in the function are disabled by making their input lines equal to 0.
• (^) This method implements the Boolean function of n variables with a 2n^ – to – 1 multiplexer.

2 nd Method for Boolean Function Implementation using Multiplexers

• (^) Boolean Function has n + 1 variables
• (^) Connect n variables to selection lines
• (^) The remaining single variable is used for the inputs of the multiplexer
• (^) If ‘A’ is this single variable, the inputs of the multiplexer are chosen to be either A or A′ or 1 or 0.
• (^) In this method, Boolean function of n + 1 variables is implemented using 2n^ to 1 line MUX.

Procedure for implementing any Boolean

function of n+1 variables using 2

n

x 1 MUX

• (^) Express the function in its sum of minterms form.
• (^) Assume that the ordered sequence of variables is ABCD…
• (^) Connect right most n-1 variables as selection lines with B connected to the high-order selection line.
• (^) The first half of minterms have ‘A’ in complemented form and the second half have ‘A’ in its true form.
• (^) List all the minterms in two rows
• (^) First row
  • (^) List all those minterms where A is complemented
• (^) Second row
  • (^) List all those minterms where A is uncomplemented.

Example F = Σ(1, 3, 5, 6)

Examples

• (^) Implement using Multiplexers
  • (^) F (A,B,C,D)= Σ(0,1,3,4,8,9,15)
  • (^) F(A,B,C) = Σ(1,3,5,6) with C as input variable
  • (^) Construct 8 x 1 MUX with dual 4 line to 1 line mux having separate enable inputs but common selection lines. use a block diagram construction.