1. A half adder is a circuit that adds two bits to give a sum and a carry.Give the truth table for a half adder, and design the circuit using only two gates.Then design a circuit which will find the 2's complement of a 4-bit binary number. Use four half adders and any additional gates. (Hint: Recall that oneway to find the 2's complement of a binary number is to complement all bits, and then add 1.)
2. (a) Write the switching functionj (x,y) = x + y as a sum of minterms and as a product of maxterms.
(b) Consider the Boolean algebra of four elements {o, 1, a, b} specified lby the following operation tables and the Boolean functionj(x,y) = ax + by where a and b are two of the elements in the Boolean algebra .Writej(x,y) in a sum-of-minterms form.
(c) Write the Boolean function of part (b) in a product-of-maxterms form.
(d) Give a table of combinations for the Boolean function of Part (b).(Note:The table of combinations has 16 rows, notjus t 4.)
(e) Which four rows of the table of combinations completely specify the function of Part (b)? Verify your answer.
|
|
+
|
0
|
1
|
a
|
b
|
|
|
0
|
1
|
a
|
b
|
|
0
|
1
|
|
0
|
0
|
1
|
a
|
b
|
|
0
|
0
|
0
|
0
|
0
|
|
1
|
0
|
|
|
|
1
|
1
|
|
|
|
0
|
1
|
a
|
b
|
|
a
|
b
|
|
a
|
a
|
1
|
a
|
|
|
a
|
0
|
a
|
a
|
0
|
|
b
|
a
|
|
b
|
b
|
1
|
1
|
b
|
|
b
|
0
|
b
|
0
|
b
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|