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Implementation of function using mux

Implement the function F(ABCD) = ∑m(2,3,4,5,8,9,12) using a) 16:1 mux b) Using one 8: 1Mux

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The Given Function - $F(ABCD) = ∑m(2,3,4,5,8,9,12)$

## a] Implementation with 16:1 MUX

• In the given Boolean expression, there are 4 variables.
• Hence, use 2n = 24 : 1 = 16:1 multiplexer.
• So, the mux has 16 input lines, 4 selection lines, and 1 output.
• The inputs, corresponding to the min-terms (2,3,4,5,8,9,12) are connected to logic 1 and the remaining terms to logic 0 (Grounded).
• The given input variables are connected as 4 selection lines.
• The 16:1 multiplexer can be drawn as follows:

## b] Implementation with 8:1 MUX

• In the given boolean expression, there are 4 variables.
• Hence, we should use 24 : 1 = 16:1 multiplexer.
• But as per the question, it is to be implemented with 8:1 mux.
• For the 8:1 multiplexer, there should be 3 selection lines.
• So from the given 4 variables, the 3 least significant variables(B, C, D) are used as selection line inputs.
• Let us derive the eight inputs of the 8:1 multiplexer using the Implementation Table.
• The eight inputs are listed column-wise and all the minterms are written under the eight inputs in rows as shown below the implementation table:

• From the derived input, 8:1 multiplexer can be drawn as follows: