Question

(a) The truth table below shows a certain function F(P,Q,R,S).

Implement the function F using an 8:1 multiplexer, without any other logic gate. Only the constants 0 and 1, and the literals (but not their complements) are available.
Fill in the inputs in the multiplexer diagram.

(b). Implement the function F using a 24 decoder and a 4:1 multiplexer, and at most one logic gate. Only the constants 0 and 1, and the literals (but not their complements) are available. The selector inputs for the multiplexer have been filled in for you and you are not allowed to change them. Complete the diagram above.

DO D1 D2 000 01 00100 D3 D4 D5 S 010 1 D7 0100 10 0 00 10010 1000 101 110 01 110 1 |Q 0123

Answer 1

(a)Here we are going to follow one method:

1) First choose selection lines (other than MSB). Here they are QRS. Now look at truth table, when P=0 then we get QRS equal to 0 to 7 in binary format. And for P=1 also we get QRS equal to 0 to 7.

So we will make one table as following:

2) Here numbers from 0 to 15 represent the total input bits. Now we circle those bits which has output (F) equal to 1.

3) Then look at pairs(up-down), if (i) zero circles are there then write 0. (ii) only one circle is there then write P(bar) if it is on any number from 0 to 7, or write P if it is on any number from 8 to 15. (iii) Both numbers has circle then write 1 because output will be surly 1.

4) Now we get eight inputs for 8:1 multiplexer.

Now let's solve the question. Here we get P(bar) as one input so we can't use this. So let's interchange the sequence of input bits, make it QPRS and then adjust the output (F) accordingly.

Now, Solechon line = PRS -'. Gircuit diaq ram:- 0 I O11 2. 3 8-1 P R S

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