Input Inverse

Procedure

1.Fill up a truth table of the 2’s complement generator.

Input Inverse

2’s complement =Inverse +1

F0 F1 F2 F3 F4

00000 11111 0 0 0 0 0

00001 11110 1 1 1 1 1

00010 11101 1 1 1 1 0

00011 11100 1 1 1 0 1

00100 11011 1 1 1 0 0

00101 11010 1 1 0 1 1

00110 11001 1 1 0 1 0

00111 11000 1 1 0 0 1

01000 10111 1 1 0 0 0

01001 10110 1 0 1 1 1

01010 10101 1 0 1 1 0

01011 10100 1 0 1 0 1

01100 10011 1 0 1 0 0

01101 10010 1 0 0 1 1

01110 10001 1 0 0 1 0

01111 10000 1 0 0 0 1

2.Fill in a K-map for each output. Solve these K-maps and provide the reduced boolean equations that shows the behavior of the 2’s complement generator.

K map for F0 :

F0= A+B+C+D

k-map for F1 :

F1=A’D+A’C+A’B+AB’C’D’

k-map for F2 :

F2=B’D + B’C + BC’D

k-map for F4:

F4=D

3. Minimize the circuit even more, such that you use only 2 types of gates. Show your work!!

After deriving the equation using k-map we notice that there are terms that need 3 or 4 input and gate to be implemented so we will use and gates, also its in SOP form so the best way to transform or gates is to transform them to nand gates, so the functions will be constituted of nand and And gates.