# Binary numbers

## 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
0
64
0
32
0
16
0
8
0
4
0
2
0
1
0
Decimal
0
1. Is `0110103` a binary number?
1. No
• Yes
2. What is `10101` as a decimal number?
1. 21
• 10101
• 25
• 1000