Question

Calculate the sum and difference of the given 8-bit unsigned binary numbers. All calculations must be done in binary. Show your work.

Answer 1

Answer:

10010101 + 00101110 = 1 1 0 0 0 0 1 1 , 10010101 - 00101110 = 0 1 1 0 0 1 1 1,

01101101 + 01110011   = 1 1 1 0 0 0 0 0 , 01101101 - 01110011 = - 1  1 1 1  1 0 1  0

Explanation:

10010101 + 00101110 =   1 0 0 1 0 1 0 1

                                    + 0 0 1 0 1 1 1 0

                                       1 1 0 0 0 0 1 1

In binary, 1 plus 0 is 1, but 1 plus 1 ( which conventionally is two) is divided by 2 and the result is carried-out, while the remainder is used as the answer.

10010101 - 00101110 =   1 0 0 1 0 1 0 1

                                   - 0 0 1 0 1 1 1 0

                                     0 1 1 0 0 1 1 1  

Subtraction in Binary calculation, a borrow to a 0 value is equal to two, this law is implemented in a case where 1 is subtracted from 0 ( which is impossible).

01101101 + 01110011   =   0 1 1 0 1 1 0 1

                                   + 0 1 1 1 0 0 1  1

                                      1 1 1 0 0 0 0 0

01101101 - 01110011   =   0 1 1 0 1 1 0 1

                                   - 0 1 1 1 0 0 1  1

                                   - 1  1 1 1  1 0 1  0

At the end of the subtraction, if the value subtracted from in less than the subtracted number, two is borrowed and the result becomes negative or signed.