Question

Suppose we have a 10-bit computer that uses 10-bit 2's complement representation. The number representation of -35 is

• A. 0000100011
• B. 1100100011
• C. 1111011011
• D. 1111011101

Hint:

To find the 2's complement of a negative number, first convert the positive number to binary, then invert the digits (1's complement), and add 1 to the result.

Answer 1

The Correct Option is C

To find the 2's complement representation of -35 in a 10-bit system, follow these steps:
1. Start with the binary representation of 35: \[ 35 = 001000101 \] This is the 8-bit binary representation of 35. For a 10-bit representation, we add leading zeroes: \[ 35 = 00001000101 \] 2. Find the 1's complement (invert all bits): \[ 11110111010 \] 3. Add 1 to the 1's complement to find the 2's complement: \[ 1111011011 \] Thus, the 2's complement representation of -35 in a 10-bit system is \( \boxed{1111011011} \).