Question

6)Two integers A and B are stored in two’s complement format. Show how B is subtracted from A. (-23) - (+13) =(-36).

Hint: Let A = (-23) and B = (+13) and show how to do (A – B) in two’s complement format.

Use 8-bits torepresent each number in binary.Verify that your final answer in binary is equal to -36 in decimal. Show your work?

Answer 1

• 2's complement of a number obtained by adding 1 to its 1's complement
• 1's complement is calculated by inverting all 1's to 0's and all 0's to 1's
• Here A is -23 and B is 13
• 2's complement form of -23 is 1's complement of 23 +1

  

• 8 bit binary form of 23 is 00010111
• It's 1's complement is 11101000
• 2's complement form of -23=11101000+1 =11101001
• Subtraction is performed by adding 2's complement of subtrahend
• To perform (-23)-(+13), add 2's complement of +13 to -23
• 2's complement of 13 is 1's complement of 13 +1
• 8 bit binary form of 13 is 00001101

• it's 1's complement is 11110010
• 2's complement of 13 is 11110010+1=11110011
• Add 2's complement of 13 to -23
• 11101001+
• 11110011
• 11011100
• To show it is correct,convert 11011100 to its decimal form
• It is done by inverting each digit(0 to 1 and 1 to 0) and add 1
• 00100011+1=00100100
• =1x2⁵+0x2⁴+0x2³+1x2²+0x2¹+0x2⁰ = 32+4=36
• Since first digit of 11011100 is 1.So the number is negative
• Result is -36
• The answer is verified.