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Encoding hexadecimal numbers with 10 digits

Suppose we only have 10 digits: 0123456789, ordinarily used to express decimal numbers, such as:

decimal
1
12
57
128
1000
5598

Except we need to use them to express hexadecimal numbers which have 16 digits: 0123456789abcdef. Hexadecimal equivalents of the above numbers would be:

decimal	hexadecimal
1	1
12	c
57	20
128	80
1000	3e8
5598	15de

We can see that we are short by 6 digits: abcdef. We need some way to express these with the 10 digits that we do have, while still being able to express the original 10 digits.

One solution to this problem is to use digraphs.

For example, we can take 0 out of the pool of the available digits and use it as a mark to start a digraph. Once we do this, we can easily express the 16 digits as follows:

• Digits 1 thru 9 stand for themselves.
• The remaining digits are expressed by digraphs:

hexadecimal digit	decimal-encoded hexadecimal digit
0	00
a	01
b	02
c	03
d	04
e	05
f	06

Using this system we can express the numbers above as follows:

decimal	hexadecimal	decimal-encoded hexadecimal
1	1	1
12	c	03
57	20	200
128	80	800
1000	3e8	3058
5598	15de	150405

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© 2022 Darius J Chuck