Question

For a hypothetical 7-bit decimal (Base-10) computer which uses 1 bit for sign of exponent, 1 bit for magnitude of exponent, 1 bit for sign of mantissa and 4 bits for magnitude of mantissa, determine the largest and smallest numbers that can be represented.

Answer 1

bit(binary digit) is for binary numbers with base 2

7 digit decimal number with base 10

1 digit for sign of exponent

1 digit for magnitude of exponent

1 digit for the sign of mantissa

so 7-3 = 4 digits are left for magnitude of mantissa

sign of exp

sign of mantissa

magn of exponent

So Largest number = 0 0 9 9 9 9 9( 0 denotes positive number)

smallest number = 1 1 0 0 0 0 0 ( 1 denotes negative sign )

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