Lecture Quiz 15 on floating point          

What decimal number does the 32-bit floating point number 40a00000 represent?

1. Binary representation  (just the first 16 bits � you can ignore the last 16 0�s.)

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ 0  0  0  0  0  0  0  0  0  0  0 0 0 0 0 0  

2. The 8 exponent bits (circle the 8 bits above)

3. __________ The decimal value of the exponent (between 123 and 134).

4. The 23 fraction bits (circle the 23 bits above). (Hidden bit is not included.)

5. __________ The decimal value of the floating point number.

Represent the decimal number 23 as a 32-bit floating point number.

6. __ __ __ __ __ The decimal number 23 in binary 

7. __________ The decimal value of the required exponent (-123 to 134) 

8. __ __ __ __ __ __ __ __ The binary exponent (in excess 127 notation � answer between
                           0111000 and 1000111).

9. The 32-bit binary representation of the floating point number 23 (hidden bit hidden).

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ 0  0  0  0  0  0  0  0  0  0  0 0 0 0 0 0  


10. __ __ __ __ __ __ __ __ The hex representation of the floating point number 23.


decimal exponent     binary shift

123                  4 bits left
124                  3 bits left
125                  2 bits left
126                  1 bit left
127                  no shift (it is still just to the right of the hidden bit)
128                  1 bit right
129                  2 bits right
130                  3 bits right
131                  4 bits right
132                  5 bits right
133                  6 bits right
134                  7 bits right


127 decimal is 01111111 in binary
128 decimal is 10000000 in binary
129 decimal is 10000001 in binary