MadeEasy Test Series: Digital Logic - Floating Point Representation

Question

Consider a modified 8-bit floating point representation in which 1-bit for sign, 3-bit for exponent and 4-bit for significant. What will be representation for decimal value –12?

Answer 1

3 bit for exponent means Bias = 2^(3-1) - 1 = 4-1 = 3

12 = 1100 = 1.100 X 2^(3)

Exponent = Bias + 3 = 3+3 = 6 = 110

Significant = 100

Since Significant is 4 bits, we append extra 0 at the end to make it 1000

Here, number is negative so, Sign bit is 1

Thus, final representation = 1 110 1000

 

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Comments

Agree, I followed the same approach. I think this should be the answer however in made easy solution they took bias as 4 that looks wrong to me (as bias value should be 2$^{(n-1)}$-1 , where n is exponent bit). below is the solution from made easy. Please let me know if I am assuming or doing something wrong here.

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yes,the value of exponent is wrong in made easy solution

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It is not IEEE. So bias = 2^(k-1).

Only in IEEE do we take 2^(k-1)-1, because 0….0 and 1….1 are reserved.