Base Comparisons

Template:WhiteStart 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,
   but take it for education only. From QBPE 0.5 just use the new _BIN$ function.

Examples

Example

Comparing decimal, hexadecimal, octal and binary string values from 0 to 15.

tabletop$ = " Decimal | Hexadecimal | Octal | Binary " tablesep$ = "---------+-------------+-------+--------" tableout$ = " \ \ | \\ | \\ | \ \ " 'the PRINT USING template LOCATE 2, 10: PRINT tabletop$ LOCATE 3, 10: PRINT tablesep$ FOR n% = 0 TO 15 LOCATE 4 + n%, 10: PRINT USING tableout$; STR$(n%); HEX$(n%); OCT$(n%); _BIN$(n%) NEXT n%

Note

Although the decimal numbers 0-15 have a maximum width of 2 digits only, an extra space in the tableout$ template is needed when using the (fixed width string) slash output format, as STR$ values contain a leading sign placeholder space.

Decimal | Hexadecimal | Octal | Binary ---------+-------------+-------+-------- 0 | 0 | 0 | 0 1 | 1 | 1 | 1 2 | 2 | 2 | 10 3 | 3 | 3 | 11 4 | 4 | 4 | 100 5 | 5 | 5 | 101 6 | 6 | 6 | 110 7 | 7 | 7 | 111 8 | 8 | 10 | 1000 9 | 9 | 11 | 1001 10 | A | 12 | 1010 11 | B | 13 | 1011 12 | C | 14 | 1100 13 | D | 15 | 1101 14 | E | 16 | 1110 15 | F | 17 | 1111

See also

• _BIN$, HEX$, OCT$, VAL
• &H (hexadecimal), &O (octal), &B (binary)

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