Fractional-Number Formats A small computer has 16-bit registers. All numbers are

Question

Fractional-Number Formats

A small computer has 16-bit registers. All numbers are positive, so no sign bit is required.

What is the (4-hexit) hexadecimal representation of the (8+8)-bit binary fixed-point format for 21.7? Do not round.


The floating-point format is: First four bits for the exponent, and the next 12 bits for the fractional part of the significand. What is the (4-hexit) hexadecimal representation of the 16-bit floating-point format for 3.7? Do not round.
                         

Someone has half-converted rational number ‘x’ to a floating-point format. So far, we have: i) the sign is ‘+’, ii) the exponent is -4, and iii) the fractional part of the significand is ‘<1101>*’. What is the exact value of ‘x’? Express ‘x’ as a fraction reduced to its lowest terms.

Explanation / Answer

21.7 hex value is 0x41ad999a

binary form

sign exponent mantissa

0 10000011 0101101100110011010

grouping into 4 bits(hexit)

0100 0001 1010 1101 1001 1001 1010

4 1 a d 9 9 a

3.7 hex value is 0X400d99999999999a

sign exponent mantissa

0 10000000000 1101100110011001100110011001100110011001100110011010

grouping into 4 bits(hexit)

0100 0000 0000 1101 1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 1010

4 0 0 d 9 9 9 9 9 9 9 9 9 9 9 a

+1 1024   1.1101100110011001100110011001100110011001100110011010(binary)

1*2*1.85=3.7

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