Question

Convert the following hexadecimal format IEEE 754 single precision floating point numbers into decimal numbers into decimal numbers. Show every step in your calculation. [Answer to 2 decimal places is required.]

a. 0x3FC00000
b. 0xC1480000

Answer 1

To convert a hexadecimal format IEEE 754 single precision floating point number into a decimal number, you need to separate the sign, exponent, and mantissa, convert them to decimal values, and combine them to get the final decimal number.

Step-by-step explanation:

To convert a hexadecimal format IEEE 754 single precision floating point number into a decimal number, you can follow these steps:

1. Separate the sign, exponent, and mantissa from the hexadecimal number.
2. Convert the sign to a decimal sign (-1 for negative, 1 for positive).
3. Convert the exponent to a decimal number by subtracting the bias value (127 for single precision).
4. Convert the mantissa to a decimal fraction by dividing each hexadecimal digit by 16 raised to the power of its position.
5. Combine the sign, mantissa, and exponent to get the final decimal number.

For example:

a. 0x3FC00000

• Sign: +1
• Exponent: 2
• Mantissa: 0xC00
• Mantissa (decimal fraction): 0.75

Combining these values, the decimal number is:

(1) * (1 + 0.75) * (2^2) = 1.75 * 4 = 7.

b. 0xC1480000

• Sign: -1
• Exponent: 12
• Mantissa: 0x148
• Mantissa (decimal fraction): 0.0909090909

Combining these values, the decimal number is:

(-1) * (1 + 0.0909090909) * (2^12) = -1.0909090909 * 4096 ≈ -4460.78