Question

Write the decimal number as a 32bit flating point number in the ieee single precision standadrd

Answer 1

To write a decimal number as a 32-bit floating-point number in the IEEE single precision standard, you need to convert the decimal number to binary, determine the sign bit, normalize the binary representation, calculate the biased exponent, and write the 32-bit binary representation.

Step-by-step explanation:

To write a decimal number as a 32-bit floating-point number in the IEEE single precision standard, we can follow these steps:

1. Convert the decimal number to binary.
2. Determine the sign bit (0 for positive, 1 for negative).
3. Normalize the binary representation by moving the binary point to the left until there is only one digit to the left of the binary point.
4. Calculate the biased exponent by adding the number of times the binary point was moved to the left to the bias value (127 for single precision).
5. Write the 32-bit binary representation, starting with the sign bit, followed by the biased exponent (8 bits), and then the normalized mantissa (23 bits).

For example, let's convert the decimal number 3.25 to a 32-bit floating-point number:

Step 1: Convert 3.25 to binary: 11.01

Step 2: The number is positive, so the sign bit is 0.

Step 3: Normalize the binary representation: 1.101

Step 4: Calculate the biased exponent: 2 (the binary point was moved twice) + 127 = 129 (in binary: 10000001)

Step 5: Write the 32-bit binary representation: 0 10000001 10100000000000000000000