When programming, you may find that your Decimal calculation has to be converted to Hexadecimal, or vice versa, before you can use it. Digitrax provides conversion charts in some of their manuals; their Decoder manual for sure. Throttle Up! provides a really nice slide chart. If you want one of these, be sure to ask for one the next time you order a Throttle Up! sound decoder.

However, you may want to convert them yourself - without referencing a chart. It's not difficult. In fact, once you know how to do it, the hardest thing will be remembering how it starts. For this, we'll provide a clue a little later on that will be easy to remember.

Whether you're converting from Decimal to Hexadecimal or the other way around, just remember that you're converting a Base 10 number to Base 16, or vice versa. What this really means is that 10 in Decimal is 10 when you have counted all your fingers. 10 in Hexadecimal is 10 (one zero) when your space alien friend who has 8 fingers on each hand has counted all his fingers.

The main difference is that the Hexadecimal 10 (one zero; if you hear someone call Hexadecimal 10 "ten", they're dead wrong) represents 16 decimal digits. The extra digits are inserted after 9, so counting is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. From that point, it proceeds exactly like counting in decimal, but using all 16 digits again:10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20, and so all the way to FF.

FF is the highest value you'll ever encounter while programming CVs, because that's the largest value the eight bits of a CV can handle. FF, in Hexadecimal, converts to 255 Decimall.

Most of the time you'll need to convert Decimal to Hexadecimal. We'll do that now, then convert Hexadecimal to Decimal later.

Lets convert the Decimal value of 185 to Hexadecimal, for example.

Remembering that hexadecimal is base 16, all you have to do is divide 185 by 16: that's it, it's that simple.

185 divided by 16 = 11 with a remainder of 9.

At this point you need to know that all the Hexadecimal numbers involved with CVs are made up of two digits - a left and right. In the division we just did, the quotient (11) is the left digit, the remainder (9) is the right digit.

Notice that 11 is a two-digit value. That means it's one of those letter numbers: but which one? All you have to do is count from 9. If you say 9, 10, 11, that's three digits. So instead say 9, A, B: 11 = B.

Since 9, the remainder, is a single digit, use it as is.

Therefore, B is the left digit and 9 is the right digit. Therefore, 185 Decimal = Hexadecimal B9.

That's easy enough. Lets convert it back to decimal.

Again, remembering that Hexadecimal is base 16, all you have to do is multiply and add: yes, it's that simple.

First take the two digits apart. We have a B and we have a 9.

The left digit (B) is multiplied times 16, and 9 (the right digit) is added to that result.

Converting B to a decimal number is just like converting the other way. If you count to B, starting with 9, you have to say three digits; 9, A, B. So, instead of counting up though the letters, count decimal style for three digits: 9, 10, 11.

Multiplying 11 x 16 = 176; 176 + 9 = 185.

How do you remember whether to divide or multiply? Easy: Divide Decimals, Multiply Hex.