The basics of Technology Mapping in Digital Circuits

1. Generate the truth table of a given boolean expression
2. Represent the expression in terms of minterms
3. Convert each component into one of the cells of technology map.

Example 1:
a 8x1 multiplexer using a 2x1 mux:
8x1 --> a'b'c'I0 + a'b'cI1 +a'bc'I2 + a'bcI3 + ab'c'I4 + ab'cI5 + abc'I6 + abcI7
==> a'(b'c'I0 + b'cI1 + bc'I2 + bcI3) + a(b'c'I4 + b'cI5 + bc'I6 + bcI7)
==> a'(b'(c'I0 + cI1) + b(c'I2 + cI3)) + a(b'(c'I4 + cI5) + b(c'I6 + cI7))
==> a'(b'M1 + bM2) + a(b'M3 + bM4)
==> a'M5 + aM6
==> M7

Example 2:
AND gate using a 2x1 mux:
AB --> AB + A'0
So the mux will have A as the select line and B on select 1 and tie 0 on select 0

Example 3:
OR gate using a 2x1 mux:
A + B ==> 1(A + B)
==> (A + A')(A + B)
==> AA + AB + A'A + A'B
==> A + AB + A'B
==> A(1 + B) + A'B
==> A1 + A'B
So the mux will have A as the select line and tie 1 on select 1 and B on select 0