Perform the arithmetic operations (+36) + (-24) and (-35) - (-24) in binary usin

Question

Perform the arithmetic operations (+36) + (-24) and (-35) - (-24) in binary using signed 2's complement representation for negative numbers. A) Please write down the 2's complement representation for +36, -24, and -35, respectively. B) Please calculate (+36) + (-24) in binary using signed 2's complement representation for negative numbers. Note that directly giving a result in binary without any calculation steps will receive zero point. C) Please calculate (-35) - (-24) in binary using signed 2's complement representation for negative numbers. Note that directly giving a result in binary without any calculation steps will receive zero point.

Explanation / Answer

Solution:

A)

2's complement representation

36(10)= 00100100(2)

(-24)(10)= 11101000(2)

(-35)(10)= 11011101(2)

B)

36(10)= 00100100(2)

(-24)(10)= 11101000(2), this is in 2's complement, now both will be added.

00100100
11101000
-------------
1 00001100
--------------, 1 is carry over so we will just ignore that by 2's complement subtraction rules and rest will be our result.

C)

11011101
00011000, 2's complement of 11101000
------------
11110101
------------, no carry is generated this means the result is negative, now we need to perform 2's complement operation on the result as per 2's complement subtraction rules.

so the result will be 00001011, in negative which is -9 in decimal.

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