Decimal to Binary Calculator With Steps Online

A Decimal to Binary Calculator is a specialized tool designed to convert decimal numbers, which are based on the ten digits from 0 to 9, into binary numbers, a base-2 number system consisting only of 0 and 1. This conversion is crucial in the field of computer science and digital electronics where binary systems are fundamental.

Formula of Decimal to Binary Calculator With Steps

Converting decimal numbers to binary is systematic and involves several repetitive steps:

1. Initialize: Start with the decimal number you wish to convert.
2. Division: Divide this number by 2. Record the remainder (either 0 or 1) as the least significant bit (LSB) of the binary result.
3. Iteration: Use the quotient from the previous division as the new number to convert.
4. Repeat: Continue dividing the new number by 2, recording remainders, until the quotient is 0.
5. Binary Representation: The recorded remainders, read in reverse order from the last to the first, represent the binary equivalent of the original decimal number.

Table for General Terms

This table serves as a quick reference for common conversions that users might need frequently.

Example of Decimal to Binary Calculator With Steps

Let’s consider converting the decimal number 13 into binary:

1. 13 divided by 2 gives a quotient of 6 and remainder of 1 (LSB).
2. 6 divided by 2 gives a quotient of 3 and remainder of 0.
3. 3 divided by 2 gives a quotient of 1 and remainder of 1.
4. 1 divided by 2 gives a quotient of 0 and remainder of 1 (MSB).

Reading the remainders from bottom to top, the binary equivalent of 13 is 1101.

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