When we subtract -3 from 2, the answer in 2 s compliment form is a) 0001 b) 1101 c) 0101 d) 1001
The Correct Answer and Explanation is:
To subtract -3 from 2 using 2’s complement, you’re actually computing: 2−(−3)=2+3=52 – (-3) = 2 + 3 = 5
So we need to represent the result (5) in 2’s complement form, assuming we’re working in 4 bits, since the options are 4-bit binary numbers.
Step-by-Step Explanation:
1. Represent 2 in binary (4 bits):
2=00102 = 0010
2. Represent -3 in 2’s complement (4 bits):
- Start with +3 in binary: 3=00113 = 0011
- Take the 1’s complement (flip the bits): 11001100
- Add 1 to get the 2’s complement (i.e., -3): 1100+1=11011100 + 1 = 1101
So, -3 in 2’s complement is 1101.
3. Add 2 and -3:
0010+1101=11110010 + 1101 = 1111
This equals -1 in 4-bit 2’s complement — but this is not what the question is asking.
Instead, the question is:
“Subtract -3 from 2,” i.e., 2−(−3)=2+3=52 – (-3) = 2 + 3 = 5
So, we now compute 2 + 3.
4. Represent +3 in binary (4 bits):
3=00113 = 0011
5. Add:
0010+0011=01010010 + 0011 = 0101
So, the result is 0101, which is 5 in 4-bit binary.
Correct Answer:
c) 0101
Summary:
In 2’s complement arithmetic, subtracting a negative number is equivalent to addition. When subtracting -3 from 2, you compute 2 + 3, which equals 5. The binary representation of 5 in 4-bit binary is 0101. Thus, the correct 2’s complement form of the result is 0101, which matches option (c).
