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Convert each pair of decimal numbers to binary and add using 2's complement-110 and -84

Question

Convert each pair of decimal numbers to binary and add using 2's complement-110 and -84

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Solution

  1. Convert -110 to binary using 2's complement:

    • First, convert 110 to binary: 110 in binary is 1101110.
    • Next, find the 2's complement of 1101110:
      • Invert the digits: 0010001
      • Add 1: 0010001 + 1 = 0010010
    • So, -110 in 2's complement (assuming an 8-bit representation) is 11100110.

  2. Convert -84 to binary using 2's complement:

    • First, convert 84 to binary: 84 in binary is 1010100.
    • Next, find the 2's complement of 1010100:
      • Invert the digits: 0101011
      • Add 1: 0101011 + 1 = 0101100
    • So, -84 in 2's complement (assuming an 8-bit representation) is 10101100.

  3. Add the two 2's complement binary numbers:

    11100110
  • 10101100

110100010


4. Since the result is a 9-bit number, we need to discard the extra bit (leftmost bit):

110100010 (discard the leftmost bit) 10100010


5. The result in binary is 10100010. To verify, convert it back to decimal:
- 10100010 in binary is a negative number in 2's complement.
- Find the 2's complement to get the positive value:
  - Invert the digits: 01011101
  - Add 1: 01011101 + 1 = 01011110
- 01011110 in binary is 94 in decimal.
- Therefore, the result is -94.

So, the sum of -110 and -84 using 2's complement is -194.

This problem has been solved

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