Adder

Question 1
Consider an eight-bit ripple-carry 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 _________.
A
-1
B
-2
C
-3
D
-4
       Digital-Logic-Design       Adder       GATE 2016 set-2
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.
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 4-bit ripple-carry binary adder is implemented by using four full adders. The total propagation time of this 4-bit binary adder in microseconds is ____________.
A
19.1
B
19.2
C
18.1
D
18.2
       Digital-Logic-Design       Adder       GATE 2015 -(Set-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
A + B, and A – B, but not A + 1
B
A + B, and A + 1, but not A – B
C
A + B, but not A – B or A + 1
D
A + B, and A – B, and A + 1
       Digital-Logic-Design       Adder       Gate-2003
Question 3 Explanation: 
The circuits performs
1) A+B when K=0 and C0 = 0. It is binary adder which performs addition of two binary numbers.
2) A - B = A+ B' + 1 when K=1 and C0 = 1 ;
Here XOR gates produce B' if K=1. Since 1⊕b= b'.
"1" in (A+B+1) is coming from C0.
Note: 2's complement of B is (B'+1). 3) A+1 when B=0, K=0, C0= 1.
Increments A.
Question 4
The number of full and half-adders required to add 16-bit numbers is
A
8 half-adders, 8 full-adders
B
1 half-adder, 15 full-adders
C
16 half-adders, 0 full-adders
D
4 half-adders, 12 full-adders
       Digital-Logic-Design       Adder       Gate-1999
Question 4 Explanation: 
For LSB addition we do not need a full adder.
For addition of subsequent bits we need full adders since carry from previous addition has to be fed into the addition operation.
Question 5
 
A
proportional to N
B
proportional to log N
C
a constant
D
None of the above
       Digital-Logic-Design       Adder       Gate-1997
Question 6
 
A
Binary of Hex conversion
B
Binary to BCD conversion
C
Binary to grey code conversion
D
Binary to radix-12 conversion
       Digital-Logic-Design       Adder       Gate-1996
Question 6 Explanation: 
Here ф means 0.
Whenever, b2 = b3 = 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 b3 and b2 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.