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Numbers and Numerals

Introduction to Binary system

The numeral system we usually use has ten digits, from 0 to 9; for this reason, it is known as the base 10 system or the decimal number system. In this system of numeration, we create numbers using the ten digits. For example, 82 and 1024 are decimal numbers. These numbers can also be written as 82(10) and 1024(10).

Another system of numeration is the base 2 system or the binary number system. In this system, we form numbers using the two digits “0” and “1”. For example, 0(2), 1(2), 10(2), 100(2) and 101(2) are binary numbers. These are read as “zero to the base 2”, “one to the base 2”, “one zero to the base 2”, “one zero zero to the base 2” and “one zero one to the base 2”, respectively.

The following table lists a few numbers written as per the base 10 and base 2 systems.

Things

 

Unit of Things

 

Decimal

Representation

 

Binary

Representation

 

 

zero

0

0

*

one

1

1

**

two

2

10

***

three

3

11

****

four

4

100

*****

five

5

101

******

six

6

110

*******

seven

7

111

********

eight

8

1000

*********

nine

9

1001

As you can see, binary numbers (above 1) are longer than their decimal equivalents. The bigger a binary number, the longer it is. For example, we need twenty binary digits to represent one million. Binary numbers are quite difficult to understand and remember as they are strings of ones and zeros. This is why the binary system is not very useful in daily life.

Place-Value Table for the Base 2 System

Like the numbers in the base 10 system, the numbers in the base 2 system can also be put in a place-value table. The place-value table for the binary system is as follows:

Sixteens

Eights

Fours

Twos

Ones

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