2 - Binary

Step 2 - Understanding Binary Numbers


Just the sound of "binary numbers" sends pangs of fear through many people with different shades of arithmophobia (the irrational fear of numbers and arithmetic). Have no fear - or at least put your fear to rest. Binary numbers are just a different way to count. That is all. The concept is as easy as one plus one.




Appreciate that we use the decimal numbering system in our everyday lives, where our numbers are based on 10s of things - probably because we have 10 toes and 10 fingers. All the decimal system has are symbols that represent quantities. We call the straight vertical line a "1" and the round circle a "0".




That does not change with binary numbering systems.




With the decimal system, we can represent larger and larger numbers by tacking numbers together. So, there are single-digit numbers, like 1, double-digit numbers, like 12, triple-digit numbers, like 105, and so on and so on. As numbers get larger, each digit represents a progressively greater value. There is a 1's place, a 10’s place, a 100’s place and so on.










With this number, we have a 5 in the 1’s place, a 0 in the 10’s place and a 1 in the 100’s place. Hence,





1 x 100 + 0 x 10 + 5 x 1 = 105





Binary numbering systems are based on the same concept except that because the binary system only has two numbers, 0 and 1, it takes a lot more groupings to represent the same number. For example, the binary equivalent of 105 is 01101001 (actually, it would be usually written as 1101001 because just like in the decimal numbering system, leading zeros are dropped. However, we’ll keep that first zero in place in order to explain the next concept).


Once again, as binary numbers get larger, each digit represents a progressively greater value, but now the binary system has a 1’s place, a 2’s place, a 4’s place, 8’s place, a 16’s place, a 32’s place and so on.





Hence,


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


equals:


0 + 64 + 32 + 0 + 8 + 0 + 0 + 1 = 105