Question

we want to implement the function ?(?3,?2,?1,?0)=∑?(1,4,5,8,11,12,13). Assume complemented inputs are available at no cost.

c. Use Shannon’s Expansion Theorem to implement H using a 2-to-1 multiplexer with z3 as the select line, AND gates, and OR gates. Also, show the expression for H that uses Shannon’s Expansion Theorem.

d. Use Shannon’s Expansion Theorem to implement H using a 4-to-1 multiplexer with z2 and z1 as the select lines. Also, show the expression for H that uses Shannon’s Expansion Theorem.

Answer 1

a b c M Shannon decomposition. 2-to-1 mux and gates. 10010 2 0 1 0 0 3 01 4 10 0 0 abc abc abc abc M=abc + abc + abc + abc = 611 01 (bc) + a(bc + bc + bc)-

With AND OR gates abc a bc abc abc

Multiplexer as function generator ab f 21 011 101