Base Comparisons
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Comparing the Base Numbering Systems
Decimal (base 10) Binary (base 2) Hexadecimal (base 16) Octal (base 8)
0 0000 0 0
1 0001 1 1
2 0010 2 2
3 0011 3 3
4 0100 4 4
5 0101 5 5
6 0110 6 6
7 0111 7 7 -- maxed
8 1000 8 10
maxed-- 9 1001 9 11
10 1010 A 12
11 1011 B 13
12 1100 C 14
13 1101 D 15
14 1110 E 16
15 ------------- 1111 <--- Match ---> F ---------------- 17 -- max 2
16 10000 10 20
When the Decimal value is 15, the other 2 base systems are all maxed out!
The Binary values can be compared to all of the HEX value digit values so
it is possible to convert between the two quite easily. To convert a HEX
value to Binary just add the 4 binary digits for each HEX digit place so:
F A C E
&HFACE = 1111 + 1010 + 1100 + 1101 = &B1111101011001101
To convert a Binary value to HEX you just need to divide the number into
sections of four digits starting from the right(LSB) end. If one has less
than 4 digits on the left end you could add the leading zeros like below:
&B101011100010001001 = 0010 1011 1000 1000 1001
hexadecimal = 2 + B + 8 + 8 + 9 = &H2B889
See the Decimal to Binary conversion function that uses HEX$ on the &H page.
Example: Outputs all of the decimal, hexadecimal and octal digits:
PRINT " Decimal | Hexadecimal | Octal "
PRINT "---------+-------------+-------"
FOR n% = 0 TO 15
PRINT USING " ## | \\ | \\ " ; n% ; HEX$(n%) ; OCT$(n%)
NEXT n%
|
Decimal | Hexadecimal | Octal
---------+-------------+-------
0 | 0 | 0
1 | 1 | 1
2 | 2 | 2
3 | 3 | 3
4 | 4 | 4
5 | 5 | 5
6 | 6 | 6
7 | 7 | 7
8 | 8 | 10
9 | 9 | 11
10 | A | 12
11 | B | 13
12 | C | 14
13 | D | 15
14 | E | 16
15 | F | 17
|
See also
- Template:KW, Template:KW
- Template:KW (hexadecimal), Template:KW (octal), Template:KW (binary)