Tutorial Exercise 3.2: floats - using the IEEE 754 storage format

1. Storing float numbers in the IEEE 754 single-precision format

               
Give the equivalent bicimal representation of this number:

   Step 1:     
Now give just the mantissa for the normalised form of this bicimal, entering it as an unsigned binary value:

   Step 2:     
Now enter the exponent for the normalised form of the bicimal, entering the sign, + or -, and the unsigned binary integer value of the exponent: 

   Step 3:          
Now input how the sign is stored as a single bit:

   Step 4:            
Now input the IEEE 754 binary storage pattern for the number, finishing with the right-most 1
 (the rest of the storage will be filled with 0's for you if you are correct):

   Step 5:     
Finally, show how the 32-bit binary storage can be represented by 8 Hex digits:

   Step 6:      




2. Finding the float decimal value when given the storage in hex
Press the RANDOM STORAGE button to get the hex storage form of a simple-to-store decimal number.

Follow the steps to find the decimal value of this stored float number:

               
Now input the binary equivalent for the first four hex digits in this storage (the last four hex digits will always be 0 for this exercise,
 so they will be filled in for you if you input the correct binary for the first four hex digits):

   Step 1:     
Give the sign of the stored decimal by entering + or -:

   Step 2:            
Enter the eight bits storing the exponent:

   Step 3:            
Now enter the exponent as a signed decimal value: 

   Step 4:            
Give the normalised mantissa in binary, inserting the initial 1. and ending with the final 1 :

   Step 5:            
Finally, give the complete, original, signed decimal number:

   Step 6: