# How can a Number Represented without Normalization Technique?

Consider the following floating point Representation

Mantissa is pure fraction in signed magnitude form . What is the representation of the binary number 1111.1111 $\times 2^{2}$ in hexadecimal without Normalization .

My Approach

bias = 64

$(-1)^{S} (1.M)_{2} \times 2^{\text{E-bias}}$ This is normalized Representation .

But here we are asked to find the Not Normalized Representation that means we need to store 1111.1111 $\times 2^{2}$ as such . But How can this be done ?

$1.1111111 \times 2^{5}$

Do I need to add bias when storing in Not Normalized form ?

• here bias is 64 (excess 64 representation) i.e Sign is 0 , Exponent will be 69 and Mantissa is 255 [ this is same as Normalized Representation]

OR Do Not need to add bias and store number as it is ?

• here , Sign is 0 , Exponent will be 5 , Mantissa will be 255

Please confirm which is the correct Representation give some links to online resources stating the correctness of the approach as well

• Hint: $10.34 \times 10^3 = 10340$. – Yuval Filmus Jan 23 '17 at 20:47
• @YuvalFilmus , I have added some more useful work . Can you check now ? – Akhil Nadh PC Jan 24 '17 at 3:10