An Intro to Numeral Systems

A very, very short one, with a focus on binary

Constantin Stan
5 min readJul 10, 2020


Number 1
Photo by Jon Tyson on Unsplash

Mankind evolved, slowly I might say, from number system to number system and, for now, most of us adopted and use the decimal system in our everyday life.

There are many other numeral systems that we still use for specific tasks and some that are long forgotten.

We'll go through some of them.

An additive numeral system

We’ll start with the Roman numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages.

It is an additive system and has 7 symbols (I, V, X, L, C, D, and M corresponding in value to 1, 5, 10, 50, 100, 500, and 1000). The letter N was sometimes used to represent 0 as a standalone number.

The rules are the following:

  • symbols are placed ascending in value from right to left, much like it happens with decimals.
  • any symbol that has a smaller value than the previous one is subtracted from the value of the previous one

If you visit Europe you might see some letters engraved within museums, on buildings, and statues around you. Some of those letters you might also find on your wristwatch.

For example, shown below is the year 1864 (MDCCCLXIV).

Roman numerals on a clock and showing year 1864
Photo by Brady Leavell on Unsplash

Following the previously mentioned rules, MDCCCLXIV = V — I + X + L + C + C + C + D + M and its symbol-by-symbol equivalent in decimal is 1864 = 5–1 + 10 + 50 + 100 + 100 + 100 + 500 + 1000.

A decomposition of the MDCCCLXIV Roman number

As seen above, it is less verbose and easier to read or write 1864 compared to MDCCCLXIV. It is also easier for us, humans, to do some basic math with decimals (add, subtract, multiply, divide).

A curious fact is that the current infamous year, 2020, has the same length in decimal numerals as it has in Roman…