I can think of a few desirable traits for a set of hexadecimal digits:

- They should be easy to learn.
- It should be easy to write them by hand quickly without them being ambiguous or difficult to read.
- They should be representable using the common LCD/LED displays used in clocks, calculators, etc.
- They should depict their binary counterparts somehow. In software, we must sometimes translate between hexadecimal and binary, e.g. to determine whether a given bit in a given word is 1 or 0. If the oneness or zero-ness of each bit in a nibble was visibly represented in its corresponding digit, this translation would be easier.

In handwritten form:

For LCD/LED displays:

Description of This Alternative

First off, the digits for zero and one are the same as in conventional binary, octal, and decimal.

Next, a definition: the binary composition of a number is the set of integral powers of 2 that add up to that number. For example, the binary composition of 76 is the set {64, 8, 4} or {2

^{6}, 2

^{3}, 2

^{2}}, since its members are integral powers of 2 and they add to 76.

With this definition in mind, the following are true of the alternative digit for a given number 1-15:

- If one is part of a number's binary decomposition, its digit faces right otherwise it faces left. Equivalently, the digits for
__e__v__en__numbers face the same direction as 'e' and 'n', and the digits for o__dd__numbers face the same direction as 'd'. - The digit has a stroke across its base if and only if two is part of the number's binary composition.
- The digit has a stroke across its middle if and only if four is part of the number's binary composition.
- The digit has a stroke across its top if and only if eight is part of the number's binary composition.

Some Benefits of This Alternative

Because of these rules, if a hexadecimal digit is depicting a nibble of memory (e.g. in a hex dump program), one only has to look at a certain part of the digit to see if a particular bit is set to 1 or 0. Also, those of you who know about electronic logic gates can tell that the circuitry needed to take a four-bit input representing a number and light up the proper parts of an LED/LCD digit display would be a bit simpler these digits than with the conventional digits.

**Update:**I've been collaborating with Valdis Vītoliņš on a new set of alternative hexadecimal digits. They are an improvement on the digits described in this post. See this blog post.