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14 August, 21:02

Assume that our computer stores decimal numbers using 16 bits - 10 bits for a sign/magnitude mantissa and 6 bits for a sign/magnitude base-2 exponent. (The way we showed in class.) Show the internal representation of the following decimal quantities.

a. + 7.5

b. - 20.25

c. - 1/64

+5
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  1. 14 August, 21:32
    0
    a) 7.5 = 111.1*2° = 0.1111*2^3

    which can also be written as

    (1/2+1/4+1/8+1/16) * 8

    sign of mantissa:=0

    Mantissa (9 bits) : 111100000

    sign of exponent: 0

    Exponent (5 bits) : 0011

    the final for this is:011110000000011

    b) - 20.25 = - 10100.01*2^0 = - 0.1010001*2^5

    sign of mantissa: 1

    Mantissa (9 bits) : 101000100

    sign of exponent: 0

    Exponent (5 bits) : 00101

    the final for this is:1101000100000101

    c) - 1/64 = -.000001*2^0 = - 0.1*2^{-5}

    sign of mantissa: 1

    Mantissa (9 bits) : 100000000

    sign of exponent: 0

    Exponent (5 bits) : 00101

    the final for this is:1100000000100101
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