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