Computer Science – 13.3 Floating-point numbers, representation and manipulation | e-Consult
13.3 Floating-point numbers, representation and manipulation (1 questions)
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1. Convert 65536 to binary: 65536 in decimal is 10000000000 in binary.
2. Normalize the binary number: The normalized form is 1.10000000000000000000000 (we've added an implicit leading '1').
3. Determine the sign bit: Since 65536 is positive, the sign bit is 0.
4. Calculate the exponent: The exponent in the normalized form is 10. The biased exponent is (10 - 127) = -117. The exponent in binary is 01110101.
5. Determine the mantissa: The mantissa is 10000000000000000000000. Since we are using 23 bits for the mantissa, we only take the first 23 bits: 10000000000000000000000.
6. Combine the bits: The complete 32-bit representation is: 0 01110101 10000000000000000000000
7. Represent in hexadecimal: The binary representation is 0x40000000.