In class, I demonstrated the use of a mini-floating point number system using 8

Question

In class, I demonstrated the use of a mini-floating point number system using 8 bits. I had used 1 bit for the sign, 4 bits for the exponent, and 3 bits for the mantissa.

```c 0 0000 000 # would now represent the decimal value 0 ```

Answer the following questions under this new system.
a. What is the bias that would be used for the exponent?
b. How would the value 5.5 be stored in this system?
c. What decimal value would the following bit sequence represent `0 1010 100`?
d. What is the smallest positive non-zero value that can be expressed?
e. What is the largest finite value that can be expressed with this system?

Explanation / Answer

a.In a single precision floating point number s you get 8 bit in which to store exponent instead of storing that in two compliment it was decided to just to add 127 to the exponent since the lowest it could be in 8 bit signed is -127 and just store it as a unsigned number. If the stored value is larger/greater than the bias, that means the value of the exponent is positive, if it's lower/lesser than the bias, it's negative, if it's equal, it's zero.

b.0 1001 011 is the reperesnatation of 5.5

c. 84 is the decima value

d. 0 0000 001 is the smallest positive non zero value

e.0 1111 111

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