Ask Question
18 December, 01:27

Convert the following pairs of decimal numbers to 5-bit 2's-complement numbers, then add them. State whether or not overflow occurs in each case. (a) 4 and 11 (b) 6 and 14 (c) - 13 and 12 (d) - 4 and 8 (e) - 2 and - 9 (f) - 9 and - 14

+5
Answers (1)
  1. 18 December, 03:42
    0
    Step-by-step explanation:

    (a) 4 and 11

    binary equivalent of 4 in 5 bit = 00100

    binary equivalent of 11 in 5 bit = 01011

    decimal number 4 in 2's complement form = 11100

    decimal number 11 in 2's complement form = 10101

    now,

    1 1 1 0 0

    + 1 01 0 1

    1 1 000 1

    Since, we are doing addition on 5 bit numbers but the result of addition came in 6 digit, so there will be overflow.

    (b) 6 and 14

    binary equivalent of 6 in 5 bit = 00110

    binary equivalent of 14 in 5 bit = 01110

    decimal number 6 in 2's complement form = 11010

    decimal number 14 in 2's complement form = 10010

    now,

    1 1 0 1 0

    + 1 00 1 0

    1 0 1 1 0 0

    Since, we are doing addition on 5 bit numbers but the result of addition came in 6 digit, so there will be overflow.

    (c) - 13 and 12

    binary equivalent of - 13 in 5 bit = 10011

    binary equivalent of 12 in 5 bit = 01100

    decimal number - 13 in 2's complement form = 01101

    decimal number 12 in 2's complement form = 10100

    now,

    0 1 1 0 1

    + 1 0 1 0 0

    1 0 0 0 0 1

    Since, we are doing addition on 5 bit numbers but the result of addition came in 6 digit, so there will be overflow.

    (d) - 4 and 8

    binary equivalent of - 4 in 5 bit = 11100

    binary equivalent of 8 in 5 bit = 01000

    decimal number - 4 in 2's complement form = 00100

    decimal number 8 in 2's complement form = 11000

    now,

    0 0 1 0 0

    + 1 1 0 0 0

    1 1 1 0 0

    Since, we are doing addition on 5 bit numbers and the result of addition also came in 5 digit, so there will not be overflow.

    (e) - 2 and - 9

    binary equivalent of - 2 in 5 bit = 11110

    binary equivalent of - 9 in 5 bit = 10111

    decimal number - 2 in 2's complement form = 00010

    decimal number - 9 in 2's complement form = 01001

    now,

    0 0 0 1 0

    + 0 1 0 0 1

    0 1 0 1 1

    Since, we are doing addition on 5 bit numbers and the result of addition also came in 5 digit, so there will not be overflow.

    (f) - 9 and - 14

    binary equivalent of - 9 in 5 bit = 10111

    binary equivalent of - 14 in 5 bit = 10010

    decimal number - 9 in 2's complement form = 01001

    decimal number - 10 in 2's complement form = 01110

    now,

    0 1 0 0 1

    + 0 1 1 1 1

    1 1 000

    Since, we are doing addition on 5 bit numbers and the result of addition also came in 5 digit, so there will not be overflow.
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Convert the following pairs of decimal numbers to 5-bit 2's-complement numbers, then add them. State whether or not overflow occurs in each ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers