This trick can be used in reverse for converting decimal to binary, but it’s harder to do mentally as the binary numbers tend to overflow your mental registers. If you try it, it’s best to use a piece of paper and write the binary number down as you go. You’ll be writing down the digits from right (least significant) to left (most significant).

So, the procedure looks something like:

1. Start with the decimal number in your head
2. Is the current decimal number divisible by 2?
a. If so, then write down 0
b. If not, then write down 1 and subtract 1 from the mental number.
3. Divide your mental number by 2 and go back to step 2. Repeat until your mental number is 0.

It’s easy to lose track of where you are in the conversion process, so jotting notes is helpful.

Directly applying this process to hexadecimal is even harder, as it relies on the ease of dividing by two. One possible approach would be to first convert your decimal number to binary as described above and then converting each set of four binary digits to hex, starting from the right…easy enough, just memorize your single-hex-digit-to-binary conversion table.

(please notify me via email, if you happen to have a solution)

This is a good warning, though: misapplied, you can also use this trick to embarrass yourself publicly. Thanks, Herr Z.

You had me scratching my head for ten minutes wondering why I couldn’t do the conversion. It appears you have a typo: “We’ll use the binary number 1101010″ should be “We’ll use the binary number 1011010″.

With this, I intend to startle my friends and seduce my enemies at the next cocktail party.

Thanks.