Hexadecimal Number Representations

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:

$3155_{\text{dec}} = 1*2^{11} + 1*2^{10} + 0*2^9 + 0*2^8 + 0*2^7 + 1*2^6 + 0*2^5 + 1*2^4 + 0*2^3 + 0*2^2 + 1*2^1 + 1*2^0$