Editing Computer number format (section)

===Converting between bases===

{| class="wikitable" style="float: right; clear:right; margin-left:1em; text-align:right;"
|+ Table 3: Comparison of values in different bases
|-
! Decimal !! Binary !! Octal !! Hexadecimal
|-
| 0 || 000000 || 00 || 00
|-
| 1 || 000001 || 01 || 01
|-
| 2 || 000010 || 02 || 02
|-
| 3 || 000011 || 03 || 03
|-
| 4 || 000100 || 04 || 04
|-
| 5 || 000101 || 05 || 05
|-
| 6 || 000110 || 06 || 06
|-
| 7 || 000111 || 07 || 07
|-
| 8 || 001000 || 10 || 08
|-
| 9 || 001001 || 11 || 09
|-
| 10 || 001010 || 12 || 0A
|-
| 11 || 001011 || 13 || 0B
|-
| 12 || 001100 || 14 || 0C
|-
| 13 || 001101 || 15 || 0D
|-
| 14 || 001110 || 16 || 0E
|-
| 15 || 001111 || 17 || 0F
|}

{{Main | Positional_notation#Base_conversion| l1=Positional notation (base conversion) }}

Each of these number systems is a positional system, but while decimal weights are powers of 10, the octal weights are powers of 8 and the hexadecimal weights are powers of 16. To convert from hexadecimal or octal to decimal, for each digit one multiplies the value of the digit by the value of its position and then adds the results. For example:

: <math>
\begin{align}
& \text{octal } 756 \\[5pt]
= {} & (7 \times 8^2) + (5 \times 8^1) + (6 \times 8^0) \\[5pt]
= {} & (7 \times 64) + (5 \times 8) + (6 \times 1) \\[5pt]
= {} & 448 + 40 + 6 \\[5pt]
= {} & \text{decimal } 494
\end{align}
\qquad
\begin{align}
& \text{hex } \mathrm{3b2} \\[5pt]
= {} & (3 \times 16^2) + (11 \times 16^1) + (2 \times 16^0) \\[5pt]
= {} & (3 \times 256) + (11 \times 16) + (2 \times 1) \\[5pt]
= {} & 768 + 176 + 2 \\[5pt]
= {} & \text{decimal } 946
\end{align}
</math>