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

1. Oct 18, 2011

brian.L

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 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

Last edited: Oct 18, 2011
2. Oct 18, 2011

brian.L

Re: Converting binary numbers to floating point format using single-precision IEEE 75

Help is appreciated :D

3. Oct 18, 2011

Staff: Mentor

Re: Converting binary numbers to floating point format using single-precision IEEE 75

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.

4. Oct 18, 2011

brian.L

Re: Converting binary numbers to floating point format using single-precision IEEE 75

Oh, one more question. Is the question going to end up with a different result if there is mantissa?

5. Oct 18, 2011

Staff: Mentor

Re: Converting binary numbers to floating point format using single-precision IEEE 75

What do you think a mantissa is?

6. Oct 18, 2011

brian.L

Re: Converting binary numbers to floating point format using single-precision IEEE 75

Mantissa replaces any first digit that are negative into zero?

7. Oct 18, 2011