Reading Binary made easy.

Ok so after I got a cool binary watch last Christmas. I have had a lot of people ask me so how can you read that? I simply reply. It's easy, simple mathmatics. So then if the people are interested in really knowing how I explain it to them. This is what I'm about to do for you.

If you where to count in decimal. Numbers would repeat themselves every ten digits. When you where in grade school they may have talked about the ones place, tens place, hundreds place.

001(equals the number one, because the 1 is in the column furthest to the right)

010(equals 10 because the 1 is in the tens place.)

020(equals 20 because the 2 is in the tens place.)

023(equals 23 because you have a 2 in the tens place and a 3 in the ones place.)


Notice that the numbers repeat themselves. So in the Decimal system they repeat themselves every 10 times. Knowing this you take this same concept and put it into binary.

Binary
0001(equals 1 becuase it is in the ones place.)

0010(becuase there is only 2 digits, the numbers repeat every 2 times. So this number is 2.)

Because the numbers repeat themselves every 2 times. Your place values are different.
Your place values are like so.
first digit equals 1
second digit equals 2
third digit equals 4
fourth digit equals 8
fifth digit equals 16
so on.

(you should see the pattern in how the place values are set up)

Converting Binary to Decimal Fast


Okay if you haven't gotten lost yet. You are ready for converting it.

So you have. Or in decimal it is 44. You can figure that out by adding the the place values up. the first 1 starting from the left is 32 of course. the scond 1 is 8, then 4. So you add

32+8+4=44.

So now you know how to read binary. So you can use this method on any other number system. Such as a base 4 number system(roman numorals), base 8(octal) or base 16(hexadecimal)