Question

Convert each of the following 8-bit 2's complement binary numbers to decimal:

a). 10011101₂
b). 00010101₂
c). 11100110₂
d). 01101001₂

Answer 1

To convert an 8-bit 2's complement binary number to decimal, you can follow these steps: for positive numbers, convert each bit to decimal and sum them up; for negative numbers, flip the bits, add 1, and apply the same process. Using these steps, the given binary numbers can be converted to decimal.

Step-by-step explanation:

To convert an 8-bit 2's complement binary number to decimal, follow these steps:

1. For a positive binary number, simply convert it to decimal by multiplying each bit by the corresponding power of 2 and summing the results.
2. For a negative binary number (represented by the most significant bit being 1), convert the positive counterpart by flipping the bits and adding 1, and then apply the same process as a positive binary number.

Using these steps, we can convert the given numbers to decimal:

a) 10011101₂:
Since the most significant bit is 1, this represents a negative number. Flipping the bits and adding 1, we get 01100011₂, which is equivalent to 99 in decimal.

b) 00010101₂:
This represents a positive number. Converting it to decimal, we get 21.

c) 11100110₂:
Flipping the bits and adding 1, we get 00011010₂, which is equivalent to 26 in decimal.

d) 01101001₂:
This represents a positive number. Converting it to decimal, we get 105.