Computers, Counting, &

One communicates with an electronic computer by using a computer language. The computer language in turn is translated into some base system in order to direct the electrical impulses which power the computer. Base ten works very well with our pen and pencil calculations, but another base system is needed for electronic computers. If a memory device were to operate in base ten it would have to assume ten different states for the ten numerals comprising base ten (0, 1,2,3,4,5,6,7,8,9). Although this is possible with a mechanical system, it is not feasible with electricity. On the other hand, the binary base system is a perfect candidate for electronic computers. Only two numerals are used in base two (the binary base ). These are 0 and 1. These numerals can be easily represented by electricity in one of three ways:

1. by having the current either on or off,

2. by magnetizing a coil in one direction or the other,

3. by energizing or not energizing a relay

In any of the three cases, one state is taken by the numeral 0 and the other state by the numeral 1.

 

Computers do not count the way people do – one, two, three, four, five, six , seven, eight, nine, ten, eleven, twelve,... Instead, they count one, ten, eleven, one hundred, one hundred and one, one hundred and ten, one hundred and eleven,...

 

Since, computers operate with electricity. Their mechanisms use electricity to translate to symbols we can understand on their monitors. As electricity passes through the intricate parts of a computer, it can either turn a part on or off. On and off are the only two possibilities for electricity which is why only two digits , 0 and 1, and base two are used by computers.

BASE TEN vs BASE TWO

When we write our numbers we use the digits 0, 1,2, 3, 4, 5, 6, 7, 8, 9. This is called base ten because we use ten digits to form any number. The placement of the digit in the number stands for that digit times a power of ten. When we write our numbers, each digit’s value depends on its place in the number, for example,

5374 does not mean 5+ 3+ 7 + 4 , but it means
5 thousands +3 hundreds + 7 tens +4 ones.

Each place in the number is a power of ten:

thousand =1000=10x10x10=10³
hundred=100=10x10²
ten=10=10¹
one=1=10⁰

Computers write their numbers using only the digits 0 and 1. Their system is called base two because only the first two digits are used to form numbers and each place in the number is a power of two. The first place is the 1’s place, then comes the 2’s place, then the 2x2=4’s place, then the 2x2x2=8’s place, and so on.

so the number 1101 would mean

1x8 +1x4 +0x2 +1x1 = totals 13 in base ten system.