Question

About logic diagram, boolean algebra, computer organization

Draw the logic diagram for function F as a 2‐level AND‐OR circuit.

Background

F(a,b,c) --> F output 1 if abc is interpreted as 3-bit unsigned integer is a prime number. Output is 0 for other numbers.

The Simplified SOP Expression of F = a'b + ac

F (a, b, c) = m (2, 3, 5, 7)

Note:

i) complemented inputs (a', b', c') are not available;

ii) Use a fan‐in of 2 only. (i.e. AND / OR gate takes only 2 inputs).

Label the final output and all intermediate outputs. Use product/sum term, e.g. a.b.c instead of minterm/maxterm notation, e.g. m7.

Answer 1

Given that we need to design a 2 level AND-OR circuit

of F where

F(a,b,c)=$\sum$m(2,3,5,7)

SOP expression

F=a'b+ac

F is 1 when abc which is a 3-bit unsigned integer is prime

Also fan-in 2 logic gates are available

The truth table of F is

a	b	c	F
0	0	0	0
0	0	1	0
0	1	0	1
0	1	1	1
1	0	0	0
1	0	1	1
1	1	0	0
1	1	1	1

The circuit diagram is

a' NOTO AND1 a'b F=a'b+ac OR1 ac AND2 Level2 Level1

Note:-NOT gates does not count towards depth of circuit