Question

Can you write process of the question?
A fictional floating-point encoding scheme uses 1 bit for sign followed by 1 bit for the exponent and 2
bits for the mantissa. It otherwise behaves exactly like the IEEE 754 encoding scheme. List down all
decimal values that can be represented by this scheme along with their binary representation.

Answer 1

Sign = 1 bit

exponent = 1 bit

Mantissa = 2 bits

Now Bias = 2^n-1 - 1 = 2^1-1 - 1 = 1-1 = 0

Possible values of 4 bits:-

1) 0000 = + 0

2) 0001 = denormalised as per IEEE 754 so value is + 2⁰x0.01 = +0.25

3) 0010 = denormalised as per IEEE 754 so value is + 2⁰x0.10 = +0.5

4) 0011 = denormalised as per IEEE 754 so value is + 2⁰x0.11 = +0.75

5) 0100 = +infinity according to IEEE 754

6)  0101 = Not a number(NAN) aacording to IEEE 754

7) 0110 = Not a number(NAN) aacording to IEEE 754

8) 0111 = Not a number(NAN) aacording to IEEE 754

9) 1000 = -0

10) 1001 = denormalised as per IEEE 754 so value is - 2⁰x0.01 = -0.25

11) 1010 = denormalised as per IEEE 754 so value is - 2⁰x0.10 = -0.5

12) 1011 = denormalised as per IEEE 754 so value is - 2⁰x0.11 = -0.75

13) 1100 = - infinity according to IEEE 754

14) 1101 = Not a number(NAN) aacording to IEEE 754

15) 1110 = Not a number(NAN) aacording to IEEE 754

16) 1111 = Not a number(NAN) aacording to IEEE 754