digital logic doubt

Question

 

Answer 1

Nothing is mentioned about positions of the fields.

Assuming fields to be in Sign, Exponent, Mantissa order.

Sign =0.

0.375= 0.25+0.125 which in binary base is 0.011. But we can't simply write 011 in mantissa as it is normalized form, need to consider implicit 1 also.

If we consider exponent as  001 (1 in decimal) and mantissa as 100 (4 in decimal) we will get number as:

+ 1.100 * 2^(1-3) = +1.100 * 2^(-2) = +0.011 (0.375 in decimal) this is what we were looking for.

Hence all the fields will be 0 001 100.  B matches.

Comments

hey I got

0 101 011

 mantissa is 011 right ?? how you convert 011 as 100 can you explain ? ..i didn't understand that

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if you take mantissa as 011 it would be 0.01011 = 0.34375 this is not we are looking for. We have to adjust implicit 1 with the use of exponent in such a way that we get 0.375.

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Utkarsh Joshi

In this question they didn't mention anywhere that whether it's a  implicit Normalization or explicit Normalization right ???

whenever they didn't mention anything we always take Explicit Normalization which is

(-1)^s (0.M) 2 ^{E - excess 3}

therefore answer should be  0 101 011

 

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Magma what does normalized form mean??

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@Magma

(0.375)₁₀ = (0.011)₂

Since standard normalized form is 1.M so we need to get 1 to the left of the binary point.

(0.011)₂ = 1.1 x 2^-2 [Shifting the point by two places towards right]

Now to get it to the form (-1)^Sx 1.M x 2^E-3

E-3=-2 => E=1

S(3 bits)	E(3 bits)	M(3 bits)
0	001	100

0001100 (B)

 

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 whenever they used the term  Normalized form we take "Implicit Normalized form " ??

but some of the question they mention Explicit normalized form...that's where I'm confused

but now my doubt is  clear  thanks  MiNiPanda