Question

Assume numbers are represented in 8-bit twos complement representation. Show the calculation of the following: a. 6 - 13?

Answer 1

To calculate 6 - 13 in 8-bit two's complement, 6 is represented as 00000110, and -13 as 11110011. Adding these gives 11111001, which corresponds to -7 after bitwise inversion and adding 1.

Step-by-step explanation:

To calculate 6 - 13 using 8-bit two's complement representation, we follow these steps:

1. Convert the positive number 6 to its 8-bit two's complement:

• 6 in binary is 00000110.

Convert the negative number -13 to its 8-bit two's complement:

• First, find the binary representation of the positive number: 13 in binary is 00001101.
• Invert the bits: 11110010.
• Add 1 to the inverted bits: 11110011 (this is the two's complement of -13).

Add the two's complement of 6 and -13:

• 00000110 (6) + 11110011 (-13)
• --------
• 11111001

11111001 is a negative number because the leftmost bit is 1.To find its value, first invert the bits: 00000110.Then add 1: 00000111 (7 in decimal).The result is -7, so 6 - 13 in 8-bit two's complement is -7.