Hi
I'm learning to convert decimal fractions into their binary equivalent.
1: After the decimal point 2's powers are in negative: 2^1, 2^2, 2^3, ...; and this is equivalent to: 0.5, 0.25, 0.125, ....
Let's say we want to convert 0.625 into its a binary fraction.
If we subtract "0.5" or "2^1" from 0.625 we are left with 0.125 and "0.125" can be represented by 2^3.
Therefore,
0.625 = 0.5 + 0 + 0.125 = 0.101
The above example was found in a book. Suppose, we have 0.620 instead. How would we convert it into a binary fraction using the method we used above? How do I use this method so that I can deal with any given decimal number?
2: I know there is another method of repeated multiplication by 2. Though this method seems simple but it's not that much natural. Please have a look on the linked scan (or, you can check the attachment):
http://img809.imageshack.us/img809/4655/imgus.jpg
I have tried to apply repeated multiplication method to convert a decimal fraction to a binary one. In case of 0.3125 I was successful but then I tried to apply it on 0.620 without any success. It seems the method would never end.
Please help me.
Regards
PG
I'm learning to convert decimal fractions into their binary equivalent.
1: After the decimal point 2's powers are in negative: 2^1, 2^2, 2^3, ...; and this is equivalent to: 0.5, 0.25, 0.125, ....
Let's say we want to convert 0.625 into its a binary fraction.
If we subtract "0.5" or "2^1" from 0.625 we are left with 0.125 and "0.125" can be represented by 2^3.
Therefore,
0.625 = 0.5 + 0 + 0.125 = 0.101
The above example was found in a book. Suppose, we have 0.620 instead. How would we convert it into a binary fraction using the method we used above? How do I use this method so that I can deal with any given decimal number?
2: I know there is another method of repeated multiplication by 2. Though this method seems simple but it's not that much natural. Please have a look on the linked scan (or, you can check the attachment):
http://img809.imageshack.us/img809/4655/imgus.jpg
I have tried to apply repeated multiplication method to convert a decimal fraction to a binary one. In case of 0.3125 I was successful but then I tried to apply it on 0.620 without any success. It seems the method would never end.
Please help me.
Regards
PG
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