July 15, 2024

All You Need To Do About Converting Decimal To Binary

All You Need To Do About Converting Decimal To Binary

The binary (base two) number system, on the other hand, has two potential values for each place-value, which are represented as 0 or 1. Because electronic computers use the binary system as their internal language, professional computer programmers need know how to convert from decimal to binary.

To convert decimal to binary, many methods are utilised. One approach to convert decimal to binary is to divide the given decimal value by 2 recursively. The remainders are then added together until the quotient reaches zero. The binary value of the specified decimal number is then obtained by rewriting the remainders in reverse order.

A number system is a way of mathematically representing numbers using a set of digits or symbols.The decimal number system, binary number system, octal number system, and hexadecimal number system are examples of different number systems. These are recognised by the base that they possess. Numbers may be readily translated from one base to another with the use of a few formulas.

Converting Decimal to Binary

Every number system has a base that is determined by the total number of digits employed in the system.Because it only uses two digits to express a number, the binary number system has a base of two. Similarly, the decimal number system has a base of ten since each number is represented by ten digits. 

Short Division by Two with the Remainder

This approach is considerably easier to comprehend when depicted on paper, and it depends solely on division by two, making it ideal for novices.

Write the divisor as the base of the destination system outside the curve of the division sign (in our example, “2” for binary).

Write the number of the base system you’re dealing with as a subscript of each number to minimise misunderstanding before and after conversion.


Under the long division sign, write the integer answer (quotient), and the remainder (0 or 1) to the right of the dividend.

Because we’re dividing by 2, if the dividend is even, the binary remainder will be 0, and if it’s odd, the binary remainder will be 1.

Continue dividing until you get to zero. 

Continue dividing each new quotient by two and writing the remainders to the right of each payment. When the quotient reaches 0, come to a halt.

Create a new binary number and write it down. Start from the bottom and work your way up to the top, reading the remainders in order. You’ll need 10011100 for this example. 

This technique may be tweaked to convert any base to decimal. The divisor is 2 since the desired destination is base 2. (binary).. Replace the 2 in the technique with the desired base if the target destination is a different base.

Definition of the Decimal Number System

It is also known as the Hindu-Arabic number system in which each digit has a location and it is 10 times more significant than the preceding digit. Decimal fractions are also denoted with a decimal point. For example, in the decimal number 36, 3 is 10 times greater than 6. Decimal numbers include 4510, 11810, and so on. It is the most extensively used number system, with numbers that are clearly identifiable even when the base is not displayed.

This was all about the concept of decimal to binary. All you need to do is to enrol in the Cuemath classes. All the experts from our team will help you out and give you the knowledge so that you can have complete understanding in the best manner. 

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Anshu Dev

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