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23 June, 11:47

Because A-B=A + (-B), the subtraction of signed numbers can be accomplished by adding the complement. Subtract each of the following pairs of 5-bit binary numbers by adding the complement of the subtrahend to the minuend. Indicate when an overflow occurs. Assume that negative number are represented in 1's complement. Then repeat using 2's complement.

a) 01001-11010b) 11010-11001c) 10110-01101d) 11011-00111e) 11100-10101

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  1. 23 June, 14:11
    0
    Using 1's complement

    a)

    Therefore the difference is - 10001

    b)

    Therefore the difference is 00001

    c)

    Therefore the difference is 01001

    d)

    Therefore the difference is 10100

    e)

    Therefore the difference is 00111

    Explanation:

    Using 1's complement

    a) The 1's complement of the subtrahend 11010 = 00101.

    Therefore 01001-11010 = 01001 + 00101 = 01110

    Since no overflow, we take the 1's complement of the result and it is negative.

    Therefore the difference is - 10001

    b) The 1's complement of the subtrahend 11001 = 00110.

    Therefore 11010-11001 = 11010 + 00110 = 1 00000

    Since there is an overflow, we add the overflow to the result

    Therefore the difference is 00001

    c) The 1's complement of the subtrahend 01101 = 10010

    Therefore 10110-01101 = 10110 + 10010 = 1 01000

    Since there is an overflow, we add the overflow to the result

    Therefore the difference is 01001

    d) The 1's complement of the subtrahend 00111 = 11000

    Therefore 11011-00111 = 11011 + 11000 = 1 10011

    Since there is an overflow, we add the overflow to the result

    Therefore the difference is 10100

    e) The 1's complement of the subtrahend 10101 = 01010

    Therefore 11100-10101 = 11100 + 01010 = 1 00110

    Since there is an overflow, we add the overflow to the result

    Therefore the difference is 00111

    Using 2's complement

    a) The 2's complement of the subtrahend 11010 = 00110.

    Therefore 01001-11010 = 01001 + 00110 = 01111

    Since no overflow, we take the 2's complement of the result and it is negative.

    Therefore the difference is - 10001

    b) The 2's complement of the subtrahend 11001 = 00111.

    Therefore 11010-11001 = 11010 + 00111 = 1 00001

    Since there is an overflow, we drop the overflow

    Therefore the difference is 00001

    c) The 1's complement of the subtrahend 01101 = 10011

    Therefore 10110-01101 = 10110 + 10011 = 1 01001

    Since there is an overflow, we drop the overflow

    Therefore the difference is 01001

    d) The 1's complement of the subtrahend 00111 = 11001

    Therefore 11011-00111 = 11011 + 11001 = 1 10100

    Since there is an overflow, we drop the overflow

    Therefore the difference is 10100

    e) The 1's complement of the subtrahend 10101 = 01011

    Therefore 11100-10101 = 11100 + 01011 = 1 00111

    Since there is an overflow, we drop the overflow

    Therefore the difference is 00111
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