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What is Binary Number System?

Before answering this question let us first recall what a decimal number system is. So a decimal number system is a type of number system where every digit of the number is from 0 to 9. Â Here are a few examples of a decimal number: 1,10,123,1456 etc.

Similar to a Decimal number system we have something called a Binary number system in which each digit of the number can be either 0 or 1. Here are a few examples of a binary number : 1010, 1000, 1111,1 etc.

Base of a Number System:Â

We define the base of a number as the total number digits used in the system.Â

For example: For a decimal number system we can use digits from 0 to 9 , therefore the total number of digits Â is 10, and hence the base is 10.

Similarly for a Binary number system we can use 0 or 1 , therefore the total number of digits Â is 2, and hence the base is 2.

But why are Binary Numbers so Important? Why does a computer only understand binary?

This is because a computer is an electrical device and all that an electrical device understands is electrical signals, so if we have to give an input to the computer there would only be two states possible, either there is current or there is no current.

Writing numbers in Binary number system and converting Binary numbers to Decimal.

First letâ€™s recall how we used to write numbers in decimal representation.

Eg: Representing 1234 in the decimal number system.

1 x 1000 + 2 x 100 + 3 x 10 + 4 x Â 1 = 1234Â

We would follow the same procedure for a binary number. The only difference is that instead of powers of 10 we would have powers of 2 and the digits can only be 0 or 1.

Eg: Letâ€™s suppose we are given a binary number â€˜11101â€™ and want to convert it into decimal.

Therefore the number in binary is = 1 x 16 + 1 x 8 + 1 x Â 4 + 2 x 0 + 1 x 1
Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  = 29

Therefore (11101)2 = 2910

Learn this and a lot more with Scaler Academy's industry vetted curriculum which covers Data Structures & Algorithms in depth.

Bit Manipulation Problems

Bit play
Problem Score Companies Time Status
Number of 1 Bits 200 8:47
Trailing Zeroes 200 14:49
Reverse Bits 225 23:50
Divide Integers 250 68:04
Different Bits Sum Pairwise 300 51:29
Bit tricks
Problem Score Companies Time Status
Min XOR value 200 37:42
Count Total Set Bits 200 63:58
Palindromic Binary Representation 200 60:51
XOR-ing the Subarrays! 200 33:32
Bit array
Problem Score Companies Time Status
Single Number 275 11:53
Single Number II 275 39:22

Problem Score Companies Time Status
Bit Flipping 200 21:30
Swap Bits 150 26:16
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