Binary numbers

Introduction
Binary counting
Binary to decimal demonstration

Introduction

Binary number system was invented by Gottfried Leibniz. As the word is prefixed with ‘Bi’ which is a Latin word and means ‘two’ in English. This brings us to the first two digits i.e., 0 and 1 which means that while counting in binary you cannot exceed 1. Infact all the numbers which you represent are made up of only two digits i.e., 0 and 1 which is quite interesting. Check out the binary representation of a decimal number (the numbers used for counting i.e., from 0-9) in binary.

Example:
Decimal Number :: 25 
Binary Number :: 11001 

Binary counting

How do we count using binary?

It is just like counting in decimal except we reach 10 much sooner.

Binary	Explanation
0	Start at 0
1	Then 1
???	But then there is no symbol for 2 … what to do?

Well how do we count in Decimal?

Decimal	Explanation
0	Start at 0
1	Then 1
2-8	Count 1,2,3,4,5,6,7,8
9	This is the last digit in Decimal
10	Start from back at 0 again, but carry 1 on the left

The same thing is done in Binary …

Binary	Explanation
0	Start at 0
1	Then 1
10	Now start back at 0 again, but carry 1 on the left
11	1 more
???	But NOW what … ?

What happens in Decimal?

Decimal	Explanation
99	When you run out of digits, …
100	… start from back at 0 again, but carry 1 on the left

And that is what is done in Binary …

Binary	Explanation
0	Start at 0
1	Then 1
10	Now start back at 0 again, but carry 1 on the left
11	1 more
100	start back at 0 again, and carry one to the number on the left but that number is already at 1 so it also goes back to 0 and 1 is carried to the next position on the left
101
110
111
1000	Start back at 0 again (for all 3 digits), add 1 on the left

Binary to decimal demonstration

Let’s tell you something more about conversion. Conversion from Binary to Decimal is quite a simple task. All you need to do is begin from the right. Follow the steps below:

STEP 1: Write the decimal value of each digit on top of them respectively. The value which you seek to write is 2^{(place value from right)} beginning from 0 i.e., 2⁰, 2¹, 2² …. continuing up to 2⁷.
STEP 2: Now, multiply each digit of binary number with its value.
STEP 3: Add ‘em all.
STEP 4: Result is ready :)

Note: If the number is large, increase bits of the binary number on the left. Keep in mind that it’s value will increase subsequently.

Example ::
Decimal number :: 25
You can convert the 1st, 4th, and the 5th digit from the right by tapping on it to convert from 0 to 1.
Further, the respective binary digit is multiplied with the value present on top of each digit. Now add.
In this Case ::
1x16 + 1x8 + 0x4 + 0x2 + 1x1 = 25 which is the decimal equivalent of the binary number 11001

Use the Simulator below to get the decimal equivalent of a binary number

Click on the ‘0’ to change it to ‘1’ and vice-versa

Binary

128

Decimal

Is 0110103 a binary number?
1. No
  - Yes
What is 10101 as a decimal number?
1. 21
  - 10101
  - 25
  - 1000