Hexadecimal Number Representations
Learn to represent numbers in a hexadecimal base system and why this number system is so useful.
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Hexadecimal representation (base sixteen)
If we can count up to sixteen, twelve stones fit in one group, but we need more symbols:
$A, B, C, D, E,$ and $F$ for ten, eleven, twelve, thirteen, fourteen, and fifteen, respectively.
Examples:

$12_{\text{dec}} = C\space\space$ in hexadecimal representation (notation)

$123_{\text{dec}} = (7*16^1 + 11*16^0)_{\text{dec}} = (7B)_{\text{hex}}$
Formulas:
Using the summation symbol, we have this formula:
$N_{\text{dec}}=\sum_{i=0}^n a_i*16^i$
Why are hexadecimal numbers used?
Consider a number written in binary notation: $110001010011_2$. Its equivalent in decimal notation is $3155$. We can decompose the number with binary coefficients as follows:
$3155_{\text{dec}} = 1*2^{11} + 1*2^{10} + 0*2^9 + 0*2^8 + 0*2^7 + 1*2^6 + 0*2^5 + 1*2^4 + 0*2^3 + 0*2^2 + 1*2^1 + 1*2^0$
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