The following are the four important types of number systems.

1. Decimal
2. Binary
3. Octal
4. Hexadecimal

In this article, we’ll look at Decimal and Binary Number Systems. We’ll discuss the other two number systems in our next article.

Decimal System

‘Deci’ means ten. The decimal number system has ten as its base. It uses ten digits from 0 to 9. The decimal number system is also called Hindu Arabic, or Arabic, or base 10 system.

The decimal system is simple and versatile. It is the most commonly used number system. It has become the dominant number system in the world. Any number, no matter how large or small, can be written in the decimal system using only the 10 basic symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. For example, the population of Asia is about 3,800,000,000. The diameter of an iron atom is about 0.000000025 cm.

It is believed that the decimal system is based on 10 digits because humans have 10 fingers and 10 toes. The word digit is derived from the Latin word ‘digitus’ which means finger or toe.

The decimal system is a positional number system. Each digit in a number has a value dependent on its position in the number. A digit's value is the digit multiplied by a power of ten according to its position in the number.

For example, consider the number 9,364.

The digit 9 is in the ‘thousands place’ and its value is 9 × 1,000 = 9,000.
The digit 3 is in the ‘hundreds place’ and its value is 3 × 100 = 300.
The digit 6 is in the ‘tens place’ and its value is 6 × 10 = 60.
The digit 4 is in the ‘ones place’ and its value is 4 × 1 = 4.

So:

9,364 = 9 × 1,000 + 3 × 100 + 6 × 10 + 4 × 1 = 9,000 + 300 + 60 + 4

In the decimal system, place values increase from right to left by powers of 10 (…1000, 100, 10, 1…). That is, from right to left a decimal system has a ones place, a tens place, a hundreds place, a thousands place, a ten thousands place etc.

For example,

In the number 22:

The 2 on the left is in the "tens place," and its value is 2 × 10 = 20.
The 2 on the right is in the "ones place," and its value is 2 × 1 = 2.

Observe that the value of the 2 on the left is 10 times as large as that of the 2 on the right.

Let’s now talk about decimal fractions.

A decimal fraction is a number with a decimal point in it, like 0.3, 0.75, 1.23, 7.049, 0.0058 etc.

In a decimal fraction (commonly called a decimal) a decimal point separates the whole numbers from fractions. The decimal point indicates the place where values change from positive to negative powers of 10. Each place to the left of the decimal point represents a positive power of 10 (10, 100, 1000, 10000, and so on) and each place to the right of the decimal point represents a negative power of 10 [10^ (-1), 10^ (-2), 10^ (-3), 10^ (-4), and so on]. When a base is raised to a negative power, it just means the reciprocal of the base raised to the positive power. So:

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