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Re: Binary base tutorial
Posted By: Paul A., on host 130.95.128.6
Date: Friday, August 20, 1999, at 02:26:40
In Reply To: Re: Binary base correction posted by Chris on Thursday, August 19, 1999, at 22:15:06:

> I've been wondering-- is there an EASY way to count in binary? And transcribe numbers the other
> way 'round? 'Cause I always end up going 1, 10, 11.... I think that's right.

1, 10, 11, 100, 101, 110, 111, 1000,...


Transcribing binary into decimal is easy.
In decimal 10 = 10^1, 100 = 10^2, 1000 = 10^3, etc.
In binary 10 = 2^1, 100 = 2^2, 1000 = 2^3, etc.

So, for example:

10110 (binary) = 10000 + 100 + 10 (binary) = 16 + 4 + 2 (decimal) = 22


Transcribing decimal into binary is a bit trickier.
Let's try it with 42.

The largest power of 2 that's not larger than 42 is 32 (100000 in binary).
42 - 32 = 10
The largest power of 2 that's not larger than 10 is 8 (1000 in binary).
10 - 8 = 2
The largest power of 2 that's not larger than 2 is 2 (10 in binary).
2 - 2 = 0

So 42 (decimal) = 101010 (binary)


Hope that helps.

Paul

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