Question

Do the following addition/subtraction problems in two’s complement binary (show your work) assuming 8 bit operands/result. If overflow happens, indicate it and explain why you think it’s overflow.

a. 125-101
b. 138+146

Answer 1

The student's question involves performing binary addition and subtraction using two's complement. The first problem 125-101 results in no overflow with an answer of 24, while the second problem 138+146 results in an overflow because both operands are positive but the result indicated a negative number.

Step-by-step explanation:

The question involves two's complement binary addition and subtraction using 8-bit operands. Here's the step-by-step process:

Procedure for a. 125-101

• Convert both numbers to 8-bit two's complement binary:
  
  • 125 in binary: 01111101
  • 101 in binary: 01100101
• Subtract 101 from 125 by adding the two's complement (invert and add 1) of 101:
  
  • Two’s complement of 101: 10011011
  • Addition: 01111101 + 10011011
• Perform binary addition:
• The sum is 00010100, which is 20 in decimal, so the result is 125 - 101 = 24.
• There is no overflow, since the sign bit did not change after the operation.

Procedure for b. 138+146

• Convert both numbers to 8-bit two's complement binary:
  
  • 138 in binary: 10001010
  • 146 in binary: 10010010
• Add the binary numbers directly:
• Binary addition: 10001010 + 10010010
• The sum is 00011100, which is an incorrect result due to overflow.
• The overflow occurs because both operands were positive, yet the result implied a negative number (due to the leading 1).