Adder
Question 1 
Consider an eightbit ripplecarry adder for computing the sum of A and B, where A and B are integers represented in 2’s complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is _________.
1  
2  
3  
4 
Question 1 Explanation:
In the question, longest LATENCY means longest DELAY for the sum to get settle.
If we do 2's complement of 1 = 0000 0001, we get 1 = "1111 1111"
So, if B = 1, every carry bit is 1.
If we do 2's complement of 1 = 0000 0001, we get 1 = "1111 1111"
So, if B = 1, every carry bit is 1.
Question 2 
A half adder is implemented with XOR and AND gates. A full adder is implemented with two half adders and one OR gate. The propagation delay of an XOR gate is twice that of an AND/OR gate. The propagation delay of an AND/OR gate is 1.2 microseconds. A 4bit ripplecarry binary adder is implemented by using four full adders. The total propagation time of this 4bit binary adder in microseconds is ____________.
19.1  
19.2  
18.1  
18.2 
Question 2 Explanation:
Here, each Full Adder is taking 4.8 microseconds. Given adder is a 4 Bit Ripple Carry Adder. So it takes 4* 4.8= 19.2 microseconds.
Question 3 
A + B, and A – B, but not A + 1  
A + B, and A + 1, but not A – B  
A + B, but not A – B or A + 1  
A + B, and A – B, and A + 1

Question 3 Explanation:
The circuits performs
1) A+B when K=0 and C_{0} = 0. It is binary adder which performs addition of two binary numbers.
2) A  B = A+ B' + 1 when K=1 and C_{0} = 1 ;
Here XOR gates produce B' if K=1. Since 1⊕b= b'.
"1" in (A+B+1) is coming from C_{0}.
Note: 2's complement of B is (B'+1). 3) A+1 when B=0, K=0, C_{0}= 1.
Increments A.
1) A+B when K=0 and C_{0} = 0. It is binary adder which performs addition of two binary numbers.
2) A  B = A+ B' + 1 when K=1 and C_{0} = 1 ;
Here XOR gates produce B' if K=1. Since 1⊕b= b'.
"1" in (A+B+1) is coming from C_{0}.
Note: 2's complement of B is (B'+1). 3) A+1 when B=0, K=0, C_{0}= 1.
Increments A.
Question 4 
The number of full and halfadders required to add 16bit numbers is
8 halfadders, 8 fulladders  
1 halfadder, 15 fulladders  
16 halfadders, 0 fulladders  
4 halfadders, 12 fulladders 
Question 4 Explanation:
For Least Significant Bit we do not need a full adder since initially carry is not present.
But for rest of bits we need full address since carry from previous addition has to be included into the addition operation.
So, in total 1 half adder and 15 full adders are required.
But for rest of bits we need full address since carry from previous addition has to be included into the addition operation.
So, in total 1 half adder and 15 full adders are required.
Question 5 
proportional to N  
proportional to log N  
a constant  
None of the above 
Question 6 
Binary of Hex conversion
 
Binary to BCD conversion  
Binary to grey code conversion
 
Binary to radix12 conversion

Question 6 Explanation:
Here ф means 0.
Whenever, b_{2} = b_{3} = 1, then only 0100, i.e., 4 is added to the given binary number. Lets write all possibilities for b.
Note that the last 4 combinations leads to b_{3} and b_{2} as 1. So, in these combinations only 0010 will be added.
1100 is 12
1101 is 13
1110 is 14
1111 is 15
in binary unsigned number system.
1100 + 0100 = 10000
1101 + 0100 = 10001, and so on.
This is conversion to radix 12.
Whenever, b_{2} = b_{3} = 1, then only 0100, i.e., 4 is added to the given binary number. Lets write all possibilities for b.
Note that the last 4 combinations leads to b_{3} and b_{2} as 1. So, in these combinations only 0010 will be added.
1100 is 12
1101 is 13
1110 is 14
1111 is 15
in binary unsigned number system.
1100 + 0100 = 10000
1101 + 0100 = 10001, and so on.
This is conversion to radix 12.
There are 6 questions to complete.