Number systems also known as numeral systems or system of numeration is a way of expressing numbers is written notation in a systematic and consistent manner. Majority of the number systems use a series of one or more digits to express a unique number while other systems may employ the use of alphabetic symbols.

## Why Several Number Systems?

Numeral systems, the more common name for number systems are the root of mathematics and computation. One reason you would need more than one system of numeration is because different number systems have different characteristics of which may be suitable for one purpose of another. We will go right ahead and take a look at the list of the best known systems in no particular order.

## 1. Binary Numbers

Binary numbers system or base 2 is a common number system highly used in computing and digital electronic as well as mathematics. It traces back to the Ancient Egyptians, Chinese and Indians. Modern Binary goes back to Gottfried Leibniz.

Binary is represented in 0s and 1s and any number can be represented this way in this number system. It can also be used to represent two states such as voltages, polarities, Boolean etc. Hence its use in digital electronics. You can find out examples of how to do Binary arithmetic here.

## 2. Ternary Numbers

Ternary numbers or base 3 is the next number system. A base-three system is used in Islam to keep track of counting Tasbih to 99. It is also used to count to 100 on a single hand for counting prayers.

In analog logic, the state of the circuit is often expressed in ternary. For example in Transistor–transistor logic output is said to either be low (grounded), high, or open (high-Z). Ternary computers also use the base-3 numeral system.

## 3. Quaternary Numbers

Quaternary numbers or base 4 is the next number system. Quaternary numerals and the way genetic code is represented by DNA. Quaternary line codes have been used for data transmission since the telegraph to today’s ISDN circuits.

This number system plays friendly with Binary.

## 4. Quinary Numbers

Probably originating from our five fingers on each hand, Quinary numbers or base 5 is the next number system we are looking at.

This number system was used in several historic cultures. To not confuse this system with decimal the counting in base 5 is as follows **[0,1,2,3,4,10,11,12,13,14,20,21,22,23,2,30]**. Notice there is no “**5**“. In this system 5 is represented as 10, 10 as 20 and so on.

## 5. Senary Numbers

Senary numbers or base 6 also known as **heximal** is a number system that was made popular as it useful in the study of prime numbers where all primes in this number system end in 1 or 5.

Octal is common in computing especially on older systems. With it the handling of 12-bit, 24-bit and 32-bit Words were better handled.

## 6. Octal Numbers

Octal numbers or base 8 also known as **Oct** is a number system that plays nice with binary. It covers the digits 0 to 7. Converting from binary to Octal can be done by grouping 3 consecutive binary digits from right to left with the remaining digits being zero padded.

Octal is common in computing especially on older systems. With it the handling of 12-bit, 24-bit and 32-bit Words were better handled.

The movie Avatar depicted the fictional Na’vi race as using the Octal number system.

## 7. Decimal Numbers

Decimal numbers or base 10 is the most familiar number system to us human beings. It is also referred to as **denary**. Historically Decimal has found presence in Hindu-Arabic numeral systems as well as Roman or Chinese numerals.

Decimal is integral in calculating fractions in the decimal notation. That is a number with a fractional part written in with the whole number separated by a dot or decimal point. Example: 3.14 as the representation of PI.

## 8. Duodecimal Numbers

Duodecimal or base 12 also known as or **dozenal** is a number system with 12 as its base. The most familiar use of the duodenal number system today is in date and time. The same was the case historically. The year is divided into 12 months, each day has 24 hours with 12 hours day light and 12 hours night time. At least at the equator.

## 9. Hexadecimal Numbers

Hexadecimal or base 16 is a number system with 16 as its base. This base is also commonly known as **Hex** and is immensely popular in computing and mathematics. Hexadecimal consists of 16 distinct symbols.

In computing it is common to express hexadecimal numbers with the prefix **0x** for example **0x2A** is the written representation for **2A**.

Each hexadecimal digit represents four binary digits or bits. The reason why it is popularly used in the fields of mathematics and computing is because hexadecimal is a human friendly representation of binary values in computing and electronics.

Therefore it is much easier to map binary to hexadecimal than to decimal. That’s why decimal is normally not used in low level computing and digital electronics. Check out these examples on how to do hexadecimal arithmetic.

## 10. Vigesimal Numbers

Vigesimal or base 20 is a number system with 20 as its base. This base is not used much today but historically through the ages and several languages there are many references in language words with special representations of 20 or its multiples.

## 11. Sexagesimal Numbers

Finally Sexagesimal or base 60 is a number system with 60 as its base. Though it originated about 3000 years BC it is still used today. It is the common number system used in geographical coordinates, angles and time.

The nature of 60 makes it the perfect base to use for dealing with time. You are all familiar with how One hour is 60 minutes which in turn is sixty seconds. t also has 12 factors which you can see being visually displayed on clock faces.

You also know there are 360 degrees in a circle.