1.a. 1111
b. 10110
c. 1000000
2.a. 15
b. 27
c. 41
3.a. 1111
b. 101100
c. 11010
4.a. 111101
b. 10100
c. 110
5. clear enough
6. Using Boolean Expression, we can simplify the circuit diagram so that we can reduce the usage of the logic gate. We can also change the circuit diagram, so that with the same output, instead of using AND/OR gate, we’ll use NAND gate which is cheaper and easier to find.
7.a. x = A’B+AB+A’B’
= B(A+A’)+A’B’
= B+A’B’
b. y = A+AB’+A’B
= A(1+B’)+A’B
= A+A’B
= A+B
c. not checked
8.a. x = A’BC+AB’C+ABC+BC’
= A’BC+AC(B+B’)+BC’
= A’BC+AC+BC’
= C(A+A’B)+BC’
= C(A+B)+BC’
= AC+BC+BC’
= AC+B(C+C’)
= AC+B
b. y = B’(A+C)+C(A’+B)+AC
= AB’+B’C+A’C+BC+AC
= AB’+B’C+BC+C(A+A’)
= AB’+C(B+B’)+C
= AB’+C