Question

Determine the single precision 32-bit representation of the following decimal numbers: (50 points) 1. e. 42.424242 f. 76.2345

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Answer #1

1. 42.424242

0(sign bit which is +) 10000100(exponent which is 132) 01010011011001001101100(mantissa which is 2732652).

we can again calculate the decimal number from its binary:

(-1)bsi 2(b2(1.b22b21....o)2 (b3ob2.b23)2-127

where  b_{i} is the bit at position i.

so, (-1)0 * 2132-127 * (1.01010011011001001101100)2

which will be: 12 1.3257575035095215

which is 42.4242401

2. 76.234567 *10-15

0 (sign +) 01010011(exponent which is 83) 01010111010101000111100 (mantissa which is 2861628)

so, 83-127 (1) 23.01010111010101000111100)2 1241.341132640838623 5.68434189 1014 1.341132640838623 76.234528 * 10-15

3. 1.4345678

0 (sign +) 01111111 (exponent 127) 01101111001111111101011 (mantissa)

127-12 1 2 1.4345678091049194 11.4345678091049194 1.4345678091049194

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