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The 4 number systems — A brief introduction about them

There are many number systems in Mathematics and Computer science but 4 among them are the most recognized. This post briefly discusses about these 4 number systems.

The 4 systems – image from cuemath.

Brief structure

Sl NumberSystemBaseNumbers used
1Binary20, 1
2Octal80, 1,2,3,4,5,6,7
3Decimal100, 1,2,3,4,5,6,7,8,9
4Hexadecimal160, 1,2,3,4,5,6,7,8,9,A(value 10), B(value 11), C(value 12), D(value 13), E(value 14), F (value 15)

But how to write numbers in each system?

Consider a number…. umm… 42.How to write it? Wait, let’s check. We write the number using it’s place value in all the system.

Ok, 1st write 42 in decimal. 
42 = 4×10^1 + 2×10^0(remember, the rightmost place's value is base^0 and the power increases as we move left.. The face value of the digit is multiplied with the value of the place to  get place value). 
So the number 42 in decimal is (42)10.
Now in binary form 
42 = 1×2^5 +0×2^4+ 1×2^3 + 0×2^2+1×2^1+0×2^0.
So the number 42 in binary is (101010)2.
Now in octal. 
42 = 5×8^1 + 2×8^0.
So the number 42 in octal is (52)8.
Now in hexadecimal, 
42 = 2×16^1+10×16^0.
But the value of 10 denoted by A. 
So, 42 in hexadecimal is (2A)16

But this system takes time during converting from systems except decimal. Is there any solution? Yes, there is, but that we will post later.

stay home stay safe,



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