How to Convert Between Base Number Systems?

Generally, the binary system consists of digital numbers that describe the combination of digits 1 (One) and 0 (Zero). The binary number system was introduced by  Claude Shannon. He noticed that the on/off states of electrical circuits could approximate the true/false states of logic. He presented the idea that Boolean logic can be connected with the binary model of truth values for generating circuitry. Remember that with the development of modern computers, the binary number by romannumeralsconverter.net system is a significant element of modern circuits. Keep in mind that the binary system is related to the base, octal, and hexadecimal systems that contain many computer-related fields. Therefore, we can say that converting between number systems is an essential skill to work with computers. In this regard, a free online binary is designed to make these conversions.

📑 Contenido de la Página
  1. Convert Between Base Number Systems:
    1. Understand the base system:
    2. Convert from the source base to decimal (base 10):
    3. Convert from decimal (base 10) to the target base:
    4. Reading the remainder in reverse order:
  2. Conclusion:

Convert Between Base Number Systems:

To convert between different base number systems that include decimal (base 10), binary (base 2), octal (base 8), or hexadecimal (base 16), you have to follow the given below steps:

Understand the base system:

It is important for you to understand the base system that you are converting from and the base system you want to convert to. Each base system uses a distinct set of digits to describe numbers and you can use this online binary code translator to understand the base system.

Convert from the source base to decimal (base 10):

If you're converting from a base other than decimal, first of all, you have to convert the number to decimal. Once you have done this, then multiply each digit of the source number by the corresponding power of the base and sum them up rapidly. For example, in binary, each digit is multiplied by 2 and raised to a power:

Example: Convert binary (base 2) number 1011 to decimal (base 10)

1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0 = 8 + 0 + 2 + 1 = 11

Well, you can verify this example with the help of an online binary translator.

Convert from decimal (base 10) to the target base:

Once you have the decimal presentation, you have to convert it to the target base. Then, divide the decimal number successively by the target base that keeps way of the remainder. The remainder, read in reverse order, will form the equivalent presentation in the target base.

Example: Convert decimal (base 10) number 35 to binary (base 2)

  • 35 divided by 2 is 17 with a remainder of 1
  • 17 divided by 2 is 8 with a remainder of 1
  • 8 divided by 2 is 4 with a remainder of 0
  • 4 divided by 2 is 2 with a remainder of 0
  • 2 divided by 2 is 1 with a remainder of 0
  • 1 divided by 2 is 0 with a remainder of 1

You can solve other examples related to this step with the help of an online binary translator.

Reading the remainder in reverse order:

100011, which is the binary presentation of 35. You have to adjust for the target base: If you're converting to a base other than decimal, you may require to use additional symbols to represent digits greater than 9. For example, in hexadecimal, digits 10 to 15 are represented by the letters A to F.

Conclusion:

These steps can be applied when converting between any base number systems. You have to just keep in mind that to convert from the source base to decimal and then from decimal to the target base. Apart from that, this binary translator online for free make conversions instantly.

Relacionado

Deja una respuesta

Tu dirección de correo electrónico no será publicada. Los campos obligatorios están marcados con *

Subir

En PedrVO.com utilizamos cookies, tanto propias como de terceros para recopilar información estadística, Si continúa navegando, consideramos que acepta su uso. Leer Más