>>1641218

>>1644609

You'll notice the same pattern with decimal, except instead of starting a new column every time you double (2), you do it every time you "decuple". 10 > 100 > 1000... So binary is basically decimal if you only had two numbers to use. Normally, when writing with binary (base 2) or decimal (base 10) on paper, you write a subscript 2 or 10 next to your number. That way, you don't get the decimal number ten (10) mixed up with the binary number two (10).

Hexadecimal isn't too different, except you're now using a number base greater than 10.

Hexadecimal = 16 characters (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F)

So A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.

The special number bases are all exponents of 2 (2, 4, 8, 16...), which is why we don't use decimal, since computers are programmed in base 2. Instead, we use the closest base that's greater than our not-2-based base. And that is 16.

By using hexadecimal, numbers are shorter to write, because it takes longer to start a column. By the time decimal starts its second column at 10, hexadecimal is still on A. It only starts it's second column once it reaches decimal 16 in value (at which point, it starts a new column as 10). At decimal 100, we're only at hexadecimal 64. At hexadecimal 100, we're at decimal 256.

You can turn a hexadecimal number into decimal in the exact same method you'd use for binary.

>Rightmost side

>Assume that there are an infinite amount of 0s to the left, each representing a new column

>Instead of going 2^0, 2^1, 2^2... from right to left columns, you use 16^0, 16^1, 16^2...

>Multiply the number in that column by that exponent

So with a hexadecimal number like D3, it would be

16^0 column = 3 = 3*16^0 = 3*1 = 3*1 = 3

16^1 column = D = D*16^1 = D*16 = 13*16 = 208

3 + 208 = 211 (decimal)

Or with something like A56...

16^0 column = 6 = 6*16^0 = 6*1 = 6*1 = 6

16^1 column = 5 = 5*16^1 = 5*16 = 5*16 = 80

16^2 column = A = A*16^2 = A*256 = 10*256 = 2560

6 + 80 + 2560 = 2646