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Binary numbers

February 27, 2011 Leave a comment

Throughout my initial research into digital electronics these kept popping up so it was a vital component of understanding digital electronics that I needed.  We also had a group session where its principals were explained.  In reality it is a fairly simple concept to understand.

Binary means two, it is the ones and zeros that digital circuits and computers use.  The simple reason being there are only two states that a digital circuit can be in off or on, 1 is on and 0 is off logical really.

To convert a binary number to a decimal one is fairly easy, it works using a place value system.  It starts by going from right to left starting with the number 1 and this number is then continuously doubled.  If we take the binary number 10010011 it can be converted like this:

   128    64    32    16    8    4    2    1
1      0      0      1      0    0    1    1

If the binary value is 1 then the number it is assigned to should be added to the total likewise if it is 0 it should not be.

So in this instance the number would be 128+0+0+16+0+0+1+1      so the final total of binary number 10010011 would be 147 as a decimal number.

To reverse this process and convert decimal to binary is fairly simple also.

If I take the number  and write down my doubled numbers again.

 64   32   16   8   4   2   1

I can see that 64 into 36 does not go so it is binary number 0

there is one 32 in 36 so it would be binary                                    1

the remaining number is four of which sixteen and 8 would not go into so you would get a 0 and 0

there would be one four in 4 so binary         1

and no twos or ones left over so it would be a final 0 and 0

so 36 as a decimal number would equal binary number 0100100.

A binary number usually begins with a zero.

Easy when you know how.

Categories: Binary numbers