Converting binary numbers to floating point format using single-precision IEEE 754


by brian.L
Tags: binary, floating point, mantissa, negative, positve
brian.L
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#1
Oct18-11, 04:17 PM
P: 7
1. The problem statement, all variables and given/known data
The problem is how to begin converting 111011.0101 into floating point. I actually did begin looking at the first digit number "1" and identify that it is a negative since is one and zero is positive. Then I try working 111011.0101 separately by splitting 111011 for now and do 0101 after. I am not exactly sure if the decimal between the digits suggest a mantissa, so that is another question I need to be point out on.

Finally, believe I let the following digits 111011 represented by bits. For example: let first digit be 128, let second digit be 64, let third digit be 32, let forth digit be 16, etc.

Then I'm stuck on the part where calculation are suppose to be made?

Note: Here is the question in case I was not clear - Convert the following binary numbers to floating-point format using single-precision IEEE 754 format.
Convert your answer to hexadecimal format.


Convert this 111011.0101 to floating point.

2. Relevant equations
No equations. I'm not sure if there is suppose to be a mantissa somewhere in the digits.

3. The attempt at a solution
Unfinished solution, full calculations has not been completed yet.
1. The problem statement, all variables and given/known data
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brian.L
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#2
Oct18-11, 04:27 PM
P: 7
Help is appreciated :D
Mark44
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#3
Oct18-11, 04:30 PM
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P: 20,961
Quote Quote by brian.L View Post
1. The problem statement, all variables and given/known data
The problem is how to begin converting 111011.0101 into floating point. I actually did begin looking at the first digit number "1" and identify that it is a negative since is one and zero is positive. Then I try working 111011.0101 separately by splitting 111011 for now and do 0101 after.
Since the most-significant bit is 1, the number is considered negative. The rest of the number's bit pattern is 11011.0101, with the first 1 removed.

Your number could be written in a quasi-scientific notation as -11011.0101 X 20. You can move the binary point to the left, simultaneously adjusting the exponent on 2. This is similar to changing 120.3 X 103 to 1.203 X 105.

So -11011.0101 X 20 = -.110110101 X 25.

You're going to have to look at IEEE 754 to see what else you need to do to convert this number to a floating point format.
Quote Quote by brian.L View Post
I am not exactly sure if the decimal between the digits suggest a mantissa, so that is another question I need to be point out on.

Finally, believe I let the following digits 111011 represented by bits. For example: let first digit be 128, let second digit be 64, let third digit be 32, let forth digit be 16, etc.

Then I'm stuck on the part where calculation are suppose to be made?

Note: Here is the question in case I was not clear - Convert the following binary numbers to floating-point format using single-precision IEEE 754 format.
Convert your answer to hexadecimal format.


Convert this 111011.0101 to floating point.

2. Relevant equations
No equations. I'm not sure if there is suppose to be a mantissa somewhere in the digits.

3. The attempt at a solution
Unfinished solution, full calculations has not been completed yet.

brian.L
brian.L is offline
#4
Oct18-11, 04:37 PM
P: 7

Converting binary numbers to floating point format using single-precision IEEE 754


Quote Quote by Mark44 View Post
Since the most-significant bit is 1, the number is considered negative. The rest of the number's bit pattern is 11011.0101, with the first 1 removed.

Your number could be written in a quasi-scientific notation as -11011.0101 X 20. You can move the binary point to the left, simultaneously adjusting the exponent on 2. This is similar to changing 120.3 X 103 to 1.203 X 105.

So -11011.0101 X 20 = -.110110101 X 25.

You're going to have to look at IEEE 754 to see what else you need to do to convert this number to a floating point format.
Oh, one more question. Is the question going to end up with a different result if there is mantissa?
Mark44
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#5
Oct18-11, 04:50 PM
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What do you think a mantissa is?
brian.L
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#6
Oct18-11, 04:58 PM
P: 7
Quote Quote by Mark44 View Post
What do you think a mantissa is?
Mantissa replaces any first digit that are negative into zero?
Mark44
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#7
Oct18-11, 06:05 PM
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P: 20,961
I can tell that was totally a guess.

http://en.wikipedia.org/wiki/Significand

And since you don't seem to have much of a clue about the IEEE standard in your thread title, here's a link to a wiki article on it - http://en.wikipedia.org/wiki/IEEE_754


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