Binary numbers
Table of contents
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., 2^{0}, 2^{1}, 2^{2} …. continuing up to 2^{7}.
- 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
- Is
0110103
a binary number?- No
- Yes
- No
- What is
10101
as a decimal number?- 21
- 10101
- 25
- 1000
- 21