Decimal and Hexadecimal
Decimal is base 10. The digit positions correspond to powers of 10.
\[ \begin{aligned} 1234\,_\text{DEC} &= \underset{10^3}{\fbox{ 1 }} \underset{10^2}{\fbox{ 2 }} \underset{10^1}{\fbox{ 3 }} \underset{10^0}{\fbox{ 4 }} \\ &= 1 \cdot 10^3 + 2 \cdot 10^2 + 3 \cdot 10^1 + 4 \cdot 10^0 \\ &= 1000 + 200 + 30 + 4 \end{aligned} \]
Hexadecimal (hex) is base 16. In hexadecimal we have 16 symbols: the 10 decimal symbols (0-9) and 6 letters (A-F).
\[ \begin{array}{|c|c|} \hline \text{decimal} & \text{hexadecimal} \\ \hline 0 & 0 \\ 1 & 1 \\ 2 & 2 \\ 3 & 3 \\ 4 & 4 \\ 5 & 5 \\ 6 & 6 \\ 7 & 7 \\ 8 & 8 \\ 9 & 9 \\ 10 & A \\ 11 & B \\ 12 & C \\ 13 & D \\ 14 & E \\ 15 & F \\ \hline \end{array} \]
The digit positions correspond to powers of 16. In code, we write
hex numbers with the prefix 0x. Here are some
examples:
\[ \begin{aligned} \text{0x10} &= \underset{16^1}{\fbox{ 1 }} \underset{16^0}{\fbox{ 0 }} \\ &= 1 \cdot 16^1 + 0 \cdot 16^0 \\ &= 1 \cdot 16 + 0 \cdot 1 \\ &= 16\,_\text{DEC} \end{aligned} \]
\[ \begin{aligned} \text{0xA2} &= \underset{16^1}{\fbox{ A }} \underset{16^0}{\fbox{ 2 }} \\ &= 10 \cdot 16^1 + 2 \cdot 16^0 \\ &= 10 \cdot 16 + 2 \cdot 1 \\ &= 162\,_\text{DEC} \end{aligned} \]
\[ \begin{aligned} \text{0x29A} &= \underset{16^2}{\fbox{ 2 }} \underset{16^1}{\fbox{ 9 }} \underset{16^0}{\fbox{ A }} \\ &= 2 \cdot 16^2 + 9 \cdot 16^1 + A \cdot 16^0 \\ &= 2 \cdot 256 + 9 \cdot 16 + 10 \cdot 1 \\ &= 666\,_\text{DEC} \end{aligned} \]