How do you convert from binary to decimal?

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Our conventional numbering system is based around the idea that we can represent any number with 10 different digits arranged in a specific order. Because of this, this is called a base-10 or decimal system. In binary, we can represent any number we want with only two different numbers a 1 or 0, so it is called a base-2 system. 

Let's look at an example, first in decimal.

The number 1234 can be broken down into:

1 x 4 +

10 x 3 +

100 x 2 +

1000 x 1

or alternatively

10x 4 +

10x 3 + 

102 x 2 +

103 x 1

From this we can see the evidence of a base 10 system, each time we look at the next digit, we increase the power of the multiplier.

 

So bearing this in mind, we can look at a binary number, made of just 1's and 0's, for example 0110.

Just as above, every time we look at teh next digit, we increase the power of the multiplier BUT binary is base-2...so:

2x 0 +

2x 1 +

22 x 1+

23 x 0

And adding all these numbers up lets you convert a binary number to decimal. So 0110 in decimal is 0+2+4+0 = 6!

James T. A Level Computing tutor, A Level Electronics tutor, A Level ...

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