# How do i convert a Base-2 number into Base-10?

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Bella on 22 May 2016
Edited: dpb on 23 May 2016
If the number is 1011001 then I thought I would do 2^0+2^3+2^4+2^6= 89 then (8x10^1)+(9x10^0)= 89
Would 89 be correct or should it be -89 because it starts with a 1? or is that only for integer representation?
Stephen23 on 22 May 2016
The answer depends entirely on the number encoding scheme that you are talking about. If you only consider the binary digits as being digits of a simple integer then the decimal equivalent is 89. However if you are talking about any possible binary encoding scheme, such as those commonly used to encode signed integers or floating point values then you first have to define the encoding before you can get an answer.
dpb on 23 May 2016
Edited: dpb on 23 May 2016
In this day and age it would be unusual for the actual representation to have only 7 bits so one would presume the sign is resolved as the value is actually '0101 1001'.
That is absolutely so can't be proven from the data given, granted, but that's what my crystal ball says... :)

Todd Leonhardt on 23 May 2016
You can use bin2dec() to convert a binary number string to a decimal number like so:
x = bin2dec('0111');
In this case x == 7. bin2dec assumes you are dealing with non-negative integers.
If you have either the Communications Toolbox (bi2de) or Fixed-Point Designer Toolbox (bin), then there are some other options available to you as well.