Question

For each of the following numbers, convert them to their closest single precision IEEE 754 floating point representation. First, denote the binary values of the sign, fraction, and exponent. Then provide a 32-bit hexadecimal value. Show your steps.

Answer 1

To convert a decimal number to its closest single precision IEEE 754 floating point representation, we need to break it down into three components: sign, fraction, and exponent. Let's take an example of the decimal number 12. The final value for 12 will be 0 10001001 10000000000000000000000 = 49 80 00 00 (in hexadecimal).

Step-by-step explanation:

To convert a decimal number to its closest single precision IEEE 754 floating point representation, we need to break it down into three components: sign, fraction, and exponent.

Let's take an example of the decimal number 12:

1. 
   
3. The sign is positive, so the sign bit will be 0.
4. 
   
6. The number 12 can be represented in binary as 1100. The fraction part will be 1.1 and the exponent part will be 10 (because the decimal point is shifted 1 place to the left).
7. 
   
9. The exponent bias for single precision floating point numbers is 127. So, the unbiased exponent will be 10 + 127 = 137, which can be represented in binary as 10001001.

Now, we combine the sign bit, fraction, and exponent to get the 32-bit hexadecimal value. The final value for 12 will be:

0 10001001 10000000000000000000000 = 49 80 00 00 (in hexadecimal).