Question

Consider the eight bit signed binary number 1110 0101. Convert it to signed decimal from assuming the signed binary number is represented using one's compliment.

Answer 1

Answer:    -26

Explanation:

We have:  1 1 1 0   0 1 0 1

Since it’s one’s complement representation, then we check the very first digit to state if the number is negative or positive. Since the very first digit to the left is 1, then the number will be negative.

When it is negative, we now flip the bits, so that we get:

0 0 0 1   1 0 1 0

Notice we just turn the 1’s into 0’s and vice versa.

We now convert this binary into decimal:

We assign to each digit the corresponding power of 2.  

See it in a table:

$\begin{matrix}0&0&0&1&1&0&1&0\\2^7&2^6&2^5&2^4&2^3&2^2&2^1&2^0 \end{matrix}$

Then multiplying each digit by its corresponding power of 2 and then adding the results, we get:

$2^4+2^3+2^1$

We get:

$16+8+2=26$

Since we stated that the number is negative, then, the final result is: -26