Computers only have switches or lights for counting.

They can either be on or off, which represents 0 or 1.

When we have counted to 10, we ‘carry’ 1, & start over.

The same rule applies for computers, but they count to 1.

So it goes: 0, 1, 10, 11, 100, 101, 110, 111, 1000, etc.

In decimal that’s: 0, 1, 2, 3, 4, 5, 6, 7, 8, etc.

We have given names to the positions in decimal:

units, tens, hundreds, thousands, & so on.

In binary the positions are labelled for the decimal value:

1, 2, 4, 8, 16, 32, 64, & so on.

To convert the binary number back to decimal,

you just add up all the positions with a one.

Each time the number 1 appears in a certain place that numeric equivalent is counted, when an 0 appears that number is not counted.

So the number 12 can be written as:

00001100 or simply 1100 ( = 8 + 4). The numbers are doubled from right to left. The binary number 11 = 3, 11101 = 29. For this example (where 11101 = 29 simple table for binary counting can look like this:

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

0 0 0 1 1 1 0 1

so

16 + 8 + 4 + 1 = 29 (11101)

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

0 1 0 0 1 0 1 1

so

64 + 8 + 2 + 1 = 79 (1001011)

Clear as mud?

0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, …

We then assign these to mean 0, 1, 2, 3, 4, 5, 6, 7, 8, …

So the binary number 10 is really 2, the binary number 100 is really 4, and the binary number 1000 is really 8.

We can also add to get that 1100 = 1000 + 100, which is really 8 + 4 or 12.

I hope this helps!

Base 3 (trinary where tri is the prefix meaning 3) go through 3 symbols, then repeat. 0, 1, 2, 10, 11, 12, 20, 21, 22. etc

If you replaced numbers with letters, you would get A, B, C, AA, AB, AC, BA, BB, BC, CA, CB, CC, AAA, AAB, AAC, …

Base 2 (binary where bi is the prefix meaning 2) go through 2 symbols then repeat. 0, 1, 00, 01, 10, 11, 100, 101, 110, 111, 1000, etc.

There are other bases in programming languages specifically octal (8) and hexidecimal (16 [hexi & deci] where the use 0-9 and A-F)

It’s a “Base 2” counting system. There are only two characters. Every time you get to “1” you go to the next digit.

Just like our common “Base 10” counting system. Every time we get to “9” we start over again with the next digit. So instead of counting by tenths, you count by halves.

🙂