This converter may be used to convert numbers between most commonly used bases: decimal, binary, octal, and hexadecimal (hex).
A number system is a method of representing numbers. The same number may be expressed in different ways. For instance, ‘200’ in the decimal base we are accustomed to may be represented as ‘11001000’ in the binary base, ‘310’ in the octal base, or ‘C8’ in the hex base.
Subscripts after a number are used to indicate a base:
20010 = 110010002 = 3108 = C816
A Brief Explanation of Number Systems
Decimal Number System. This system is used extensively in everyday life and is most common. All numbers around us are expressed in this system. Each position value of a number consists of one symbol ‘0’ to ‘9’.
Binary Number System. This system is used in computing. In this system, a number is expressed using symbols ‘0’ and ‘1’.
Octal Number System. It is also sometimes used in computing. In this system, a number is expressed using symbols ‘0’ to ‘7’.
Hex Number System. This number system is most commonly used in modern PCs. For instance, it is used to code colors. #FF0000 stands for red. In this system, a number is expressed using symbols ‘0’ to ‘9’ as well as letters ‘A’ to ‘F’ representing values ‘10’ to ‘15’.
Convert Numbers to the Decimal Base
Use the below formula to convert a number from any base to decimal: multiply each position value of a number by Xn,, where X refers to the base of the original number, and n — to the position value number. Then add all the products to get the result.
abcx = (a*x2 + b*x1 + c*x0)10
Convert Decimal to Any Other Base
Divide the decimal number by the value of the new base and write down the remainder. Divide the quotient of the previous step and write down the remainder. Keep dividing the quotient until the result is ‘0’. Write down the remainders in reverse order to get the number in the new base system.
Let's convert 37510 to the octal base: