Question

F(ABCD)=£(1,3,4,11,12,13,14,15) using 8x1 MUX with A as an input variable and and BCD as selectors

Answer 1

step 1 we have to make a table.

the variables which are connected to the select lines forms the column headings to the table and the variables which are not connected to the selects lines forms the row heading.

in this case BCD is connected to select line,since we have 3 select lines so we will have 2^3 = 8 input lines. so the no. of rows of the table = 8.

as shown in figure.

step 2 calculate the corresponding decimal value as shown in table and fill in the table.(as show in above figure).

step 3 encircle the numbers in the table with max-terms given in the question i.e.  £(1,3,4,11,12,13,14,15) shown in the figure.

step 4 calculate the inputs to the multiplexer by following rules:

i) if out of 2 rows none of the digit is encircle........enter '0'.

ii) if both the rows are encircled .........enter '1'

iii) if one is encircle fill the corresponding row value i.e either A or A'.

step 5 now construct the multiplexer as shown in the figure.