Computers work with electricity which is either on or off. They are made of transistors (tiny switches) that are either open or shut. So the numbers they use only have two symbols (0 and 1) rather than the 10 that we humans usually use (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). This numbering is called Base 2 or Binary.
We normally count with 10 symbols, called Decimal or Base 10. We can get to ten things before we need to use two digits, this is probably because we have 10 fingers so we can count to 10 on our own but need a second pair of hands to count the groups of 10 up to 100. Then we would need a third pair of hands to count the 100s up to 1000, and so on. This makes our columns powers of 10: 10000, 1000, 100, 10, 1 just like we learned at primary school. 392 is 3 hundreds, 9 tens and 2 units.
It follows that in Binary we will use powers of 2 as our columns. We can count zero and one in the first column, when we have two things we need another column because we have run out of symbols in the first column. So our first column is how many single things we have and the second column is how many groups of two we have.
When we get two groups of two we need another column because we only have symbols for zero groups of two and one group of two, so we put our two groups of two together and make a group of four in the next column. We can have zero groups of four and one group of four but again, when we get two groups of four we need another column, a column for groups of eight, and so on.
Our columns are 128, 64, 32, 16, 8, 4, 2, 1. so 1101 is 1 eight, 1 four, no twos and 1 one which adds up to 13.
Because we only have two symbols, 0 and 1, it is very easy to figure out numbers in binary, you just add up the column headings with 1s in them.
128 64 32 16 8 4 2 1 1 0 1 0 0 0 1 1 10100011 is one lot of 128, one lot of 32, one lot of 2, and one lot of 1. 128 + 32 + 2 + 1 which is 163.
What about 00010010 ?
128 64 32 16 8 4 2 1 0 0 0 1 0 0 1 0 is 16 + 2 which is 18Write in the column headings (if they aren't there) and just add up the columns with the 1s in.
To go from decimal notation to binary - work your way down the columns from biggest to smallest taking off each column heading as you go if you have enough.
For example. Let's convert 43 (Forty Three) from decimal to binary. Imagine a bag with 43 things in it.
Start with the 128 column, can you make a pile of 128 things from the 43 in your bag? No, so we put a 0 and move on.
Can we make a pile of 64? No, so another 0.
Can we make a pile of 32? Yes, so we put a 1 in the 32 column. After making this pile of 32 from our 43 things, we have 11 left in the bag (43 - 32 = 11).
The next column is 16, we can't make a pile of 16 from the 11 left in the bag so we put a 0 in the 16 column.
The 8 column? Yes, so 1 in the 8 column, leaving 3 in the bag.
0 in the 4 column, 1 in the 2 column and 1 in the 1 column
128 64 32 16 8 4 2 1 0 0 1 0 1 0 1 1 So 43 is 00101011