# Convert 15.625 base 10 to a floating point number in binary form?

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## 5 Replies - 6769 Views - Last Post: 17 March 2009 - 08:58 AM

### #1 tscott

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# Convert 15.625 base 10 to a floating point number in binary form?

Posted 11 March 2009 - 07:20 PM

The problem he gave me was 15.625
THIS IS WHAT I WORKED OUT BELOW:
So I convert 15 to 1111 and .625 to 01001 so that = 1111.01001 x 2^3

MY TEACHER SAID IT SHOULD BE THIS BUT GAVE NO EXPLANATION AS TO WHY CAN SOMEONE BREAK DOWN WHAT HE SAID BELOW.

TEACHER: 15.625 should be 1111.101 instead of 1111.01001

So because the exponent is positive we add 7F and 3 which is 82.

WHY IS IT 8 BITS? I thought the left most digit had to be in 3 bit form?
**** convert 82 into 8 bits which will be 10000010

answer will be 0 10000010 11110100000000000000000
in hex: 417A0000

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## Replies To: Convert 15.625 base 10 to a floating point number in binary form?

### #2 tscott

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## Re: Convert 15.625 base 10 to a floating point number in binary form?

Posted 11 March 2009 - 07:21 PM

Please show all work I'm first a bit confused on how 0 is represented in binary is it 000 or 0000 and the .43 we are going to multiply by 2 about 5 or 6 times which I can do but if someone can just walk me through this problem step by step I'm a student trying to understand it.

Thanks

### #3 BetaWar

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## Re: Convert 15.625 base 10 to a floating point number in binary form?

Posted 11 March 2009 - 09:11 PM

Dream.In.Code has a policy by which we prefer to see a good faith effort on your part before providing source code for homework assignments. Please post the code you have written in an effort to resolve the problem, and our members would be happy to provide some guidance. Be sure to include a description of any errors you are encountering as well.

Thanks.

### #4 tscott

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## Re: Convert 15.625 base 10 to a floating point number in binary form?

Posted 11 March 2009 - 09:41 PM

there is no code that needs to be written this is a study problem for my quiz.......

### #5 BigAnt

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## Re: Convert 15.625 base 10 to a floating point number in binary form?

Posted 12 March 2009 - 07:54 AM

Dream.In.Code has a policy by which we prefer to see a good faith effort on your part before providing source code for homework assignments

Post the solution you have so far and then someone can help you where you go wrong.

If you don't know what the teacher said then go and ask the teacher, this is their job and usually happy to help you as long as you provide some effort on actually doing the assignment

### #6 krum110487

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## Re: Convert 15.625 base 10 to a floating point number in binary form?

Posted 17 March 2009 - 08:58 AM

1111.101 x 2^0 is what you have

.1 = .5
.01 = .25
.001 = .125
(you find the combination that adds up to your value, they keep being divided by two)

you need to slide the decimal aka "Radix" to the first 1 (most left 1)

.1111101 x 2^4 (I moved it left 4)

but you also need a bias of x ( depending on how many bits are in your matisis AND if your teacher wants a bias!)

4 + bias = matisis

0 0000 0000000 = 8 bias
0 00000 0000000 = 16 bias
0 000000 0000000 = 32 bias
etc...

0 1100 1111101 is the floating point representation with a bias of 8!

and without a bias

0 0100 1111101

and with leading zeros and 8 bits as the value

0 00100 11111010

This post has been edited by krum110487: 17 March 2009 - 09:11 AM