# Why is the smallest number representable by this 7-bit floating-point representation said to be 0.03125 (rather than 0.00390625)?

Here is the problem (question 1).:
https://www.docdroid.net/DHKQYka/question-1.pdf
For part b, it says that the smallest positive number that can be represented is +0.03125, which through reverse engineering I get by doing 2^(-1) * 2^(-4), which implies 1 000 1000 as the floating-point number, however I feel like...
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Here is the problem (question 1).:

https://www.docdroid.net/DHKQYka/question-1.pdf

For part b, it says that the smallest positive number that can be represented is +0.03125, which through reverse engineering I get by doing 2^(-1) * 2^(-4), which implies 1 000 1000 as the floating-point number, however I feel like it should be 1 000 0001, which would represent 2^(-4) * 2^(-4) = 0.00390625.

What am I doing wrong?

Any input would be greatly appreciated!

https://www.docdroid.net/DHKQYka/question-1.pdf

For part b, it says that the smallest positive number that can be represented is +0.03125, which through reverse engineering I get by doing 2^(-1) * 2^(-4), which implies 1 000 1000 as the floating-point number, however I feel like it should be 1 000 0001, which would represent 2^(-4) * 2^(-4) = 0.00390625.

What am I doing wrong?

Any input would be greatly appreciated!

Update:
For anyone else potentially benefiting from this post, the first/sign bit should have been 0, not 1.

Update 2:
I also meant 8-bit, not 7-bit floating-point representation.

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