Binary numeral system

Binary numeral system

Binary numerical system is a base of programming. Machine was designed to manipulate with numbers. Binary system was chosen because it is the easiest way to save numbers. If one capacitor contains charge it means it is 1 else 0.

Let’s imaging we need to save some numbers, and we do not have regular digits. For example, we can have one apple. We want to save this number somehow. We will use one regular lamp to do it.

If no apple exists, then we have:

If we have one apple:

Hope it is clear.

Now we can have up to two apples. One lamp it is not enough to save this number. So, let’s use two lamps.

There are two ways to save number with two lamps.

First way, number of turned on lamps equals number of apples we have

1.       If one lamp turned on, we have one apple
2.       If two lamps turned on, we have two apples.
3.       If no lamp turned on, we do not have an apple.

It is not the best solution of doing it. Because those two combinations are identical:

               

On both we have only one lamp turned on, which means we have one apple.

Second way, position of lamp should show another number.

One apple:

Two apples:

Lamp can have only two states: off and on. If lamp is on then we have one apple, if we need to save a higher number, we should turn on next lamp and turn off current. So, lamp in next position represent number two. If we want to save number three, we can use first lamp:

If we want to save number four, we need to have extra lamp:

Now we have one on lamp and two off lams. It is means we can add extra three combinations based from previous paragraph.

Each extra lamp represent number that twice (because binary system) higher than previous.

128	64	32	16	8	4	2	1