Decimal to Binary

What are decimal numbers?

Those are the ones we daily use in our lives, often simply called numbers. They're decimal numbers. They are based on the decimal system, which utilizes ten unique digits: 0, 1, 2, 3, and 456789. Each position in this system represents a power of ten to the digit's place value. For example, in the number 2567, '2' represents two tens of thousands; '5' represents five ten- thousand; and so on.

How Does a Decimal-to-Binary Converter Work?

Though it might sound complex, decimal to binary conversion follows a simple process. Let's break it down step by step:

Conversion Process

Start with the Decimal Number: Start with the decimal number you want to change. For instance, take the decimal number 42.

Divide by 2: Divide the decimal number in half. In this example, 42 divided by two is twenty-one.

Record the Remainder: The remainder when dividing by 2 should be noted down. Here, the remainder is 0.

Repeat the Process: Divide the quotient from step 2 by 2 and keep recording remainders until the quotient becomes zero. This gives you a string of remainders, which is your binary number.

Reverse the Remainders: The binary number is obtained by reversing the order of remainders determined in step 4.

If this method of conversion is applied to the decimal number 42, it comes out as 101010 in binary. Thus, 42 in decimal becomes 1010.

Decimal to Binary Conversion Table

FAQs

What is a decimal number?

Decimal numbers are the numbers we use in our daily lives, based on the decimal system, which uses ten unique digits (0–9). Each position represents a power of ten.

What is a binary number?

Binary numbers use a base-2 system with only two digits, 0 and 1. Each position in a binary number represents a power of two.

Why do we need to convert decimal to binary?

Converting decimals to binary is essential in digital technology and computer science because computers and digital circuits operate using binary code.

How does a decimal-to-binary converter work?

A decimal-to-binary converter divides the decimal number by 2, records the remainder, and repeats this process with the quotient until it reaches zero. The binary number is formed by reversing the order of the remainders.

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