Base Converter

Using our number system converter, you can easily change the base of any number, such as convert binary to octal or vice versa. It lets you convert between all the common number systems without computational errors.

Follow these simple steps to convert from one number system to another:

STEP 1 - Enter String

Place the “code string” you want to convert.

STEP 2 - Select Input Base

Indicate the number system in which the given string has been encoded.

STEP 3 - Specify Output Base.

Highlight the number system in which you would like to convert the given string.

The tool will automatically run to provide you with the desired result once you enter all the required information.

We define a number system as a system of writing used to express numbers consistently. The mathematical notation represents numbers in a set by consistently using digits or other symbols. It provides a unique representation of each number and represents its arithmetic and algebraic structure.

Computers use number systems to translate words into numerical values so that they can understand and execute user commands. We can also say that all the information stored on the computer is in the form of digits: 0s and 1s, and number systems represent alphabets and characters in a computer system.

Indeed, the number system is one of the most fundamental concepts a computer programmer must learn.

As we all know, computers can only understand numbers. When we type some letters or words and carry out an action on the computer, the compiler translates it into the machine language (mainly binary numbers).

In a binary number system, only a few symbols called digits represent different values based on their position in a number system.

Number systems have unique symbols for every value, and they are reliable, provide comparable values, and are easy to reproduce.

Moreover, most people are familiar with the decimal system, which is how humans count. In the decimal system, all numbers are represented by the base 10, such as 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Unlike machines, humans have a natural ability to understand and count with ten fingers, whereas machines do not have that luxury. Therefore, programmers have developed other numbers systems that the computer-based devices can understand and perform the same functions.

There are several numbers of number systems supported by computers:

• Binary

• Octal

• Decimal

• Hexadecimal.

These number series that a computer machine can understand. However, there is a question about how we can understand a language based on a computer numbers system.

For a layman, it is complex to understand programming or machine language. Indeed, programmers and computer enthusiasts can understand these languages owing to their polished skills. While some need to use online number system converter tools to understand the machine language.

Let us guide you through the manual methods you can use to convert between different base numbers. Here are some easy-to-understand examples:

• Binary to Decimal Converter

  (1011)₂ = (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = (11)₁₀

• Binary to Hexadecimal Converter

  11101001010111001

  = 1 1101 0010 1011 1001

  = 1 D 2 B 9

  = 1D2B9

• Octal to Binary Converter

  75

  = 7 5

  = 111 101

  = 111101

• Octal to Decimal Converter

  76 = (7 × 8¹) + (6 × 8⁰) = 62

• Octal to Hexadecimal Converter

  72 = 3A

• Decimal to Binary Converter

  Division by 2	Quotient	Remainder (Digit)	Bit No.
  (69)/2	34	1	0
  (34)/2	17	0	1
  (17)/2	8	1	2
  (8)/2	4	0	3
  (4)/2	2	0	4
  (2)/2	1	0	5
  (1)/2	0	1	6

  = (1000101)₂

• Decimal to Octal Converter

  Division by 8	Quotient	Remainder (Digit)	Digit #
  (1942)/8	242	6	0
  (242)/8	30	2	1
  (30)/8	3	6	2
  (3)/8	0	3	3

  = (3626)₈

• Decimal to Hexadecimal Converter

  Division by 16	Quotient	Remainder (Digit)	Digit #
  (2022)/16	126	6	0
  (126)/16	7	14	1
  (7)/16	0	7	2

  = (7E6)₁₆

• Hexadecimal to Binary Converter

  4A2

  = 4 A 2

  = 0100 1010 0010

  = 010010100010

• Hexadecimal to Octal Converter

  4B9

  = 4 B 9

  = 100 1011 1001

  = 10 010 111 001

  = 2271

• Hexadecimal to Decimal Converter

  (8D6)₁₆ = (8 × 16²) + (13 × 16¹) + (6 × 16⁰) = (2262)₁₀

In case you do not have an internet connection at the moment when you want to convert any number into another number system, you can follow the above-discussed rules. Anyhow, keep in mind that you may make mistakes in the calculation while converting a large number system manually. Thus, if you do not want an error-prone number system conversion, it would be best to use our number system converter. It will effectively convert one base into another as per the requirements.