When we perform subtraction on -7 and 1, the answer in 2’s complement form is _ a) 1010 b) 1110 c) 0110 d) 1000 In radix binary, 1101 multiplied by 1011 is a) 10001111 b) 10101010 c) 11110000 d) 11001100
The correct Answer and Explanation is:
Answer:
1. Subtraction of -7 and 1 in 2’s complement form
Correct option: b) 1110
2. Binary multiplication of 1101 and 1011
Correct option: a) 10001111
Explanation:
1. Subtraction in 2’s Complement: -7 – 1
We are performing the operation -7 – 1, which is equivalent to -7 + (-1).
To compute this in 2’s complement form, let’s assume a 4-bit system for simplicity.
Step 1: Represent -7 in 2’s complement (4-bit)
- 7 in binary =
0111 - Invert the bits:
1000 - Add 1:
1001→ So, -7 = 1001
Step 2: Represent -1 in 2’s complement (4-bit)
- 1 in binary =
0001 - Invert the bits:
1110 - Add 1:
1111→ So, -1 = 1111
Step 3: Add -7 and -1
1001 (-7)
+ 1111 (-1)
-------
11000
The result is 11000. In 4-bit representation, we drop the leftmost carry bit, resulting in 1000.
However, the question asks for -7 – 1, which is -8. Let’s check the 2’s complement of -8:
- 8 in binary =
1000 - Invert:
0111 - Add 1:
1000(already in 2’s complement form)
Thus, the correct result in 4-bit 2’s complement is: 1000
So option d) 1000 is correct (not b).
🛑 Correction: The correct answer is d) 1000, not b) 1110.
2. Binary Multiplication: 1101 × 1011
1101 (13 in decimal)
× 1011 (11 in decimal)
= 13 × 11 = 143
Now convert 143 to binary:
143 ÷ 2 = 71 R1
71 ÷ 2 = 35 R1
35 ÷ 2 = 17 R1
17 ÷ 2 = 8 R1
8 ÷ 2 = 4 R0
4 ÷ 2 = 2 R0
2 ÷ 2 = 1 R0
1 ÷ 2 = 0 R1
Reading in reverse: 10001111
✅ Hence, the correct answer is a) 10001111.
Summary
- -7 – 1 in 2’s complement (4-bit) = 1000 → Correct option: d)
- 1101 × 1011 = 10001111 (143 in binary) → Correct option: a)
