# Decimal to Binary

Decimal to Binary tool

## Decimal to Binary Conversion

If you have ever tackled any computer science problems, including coding, you may have come across decimal and binary numbers. Understanding these two numeral systems and the conversion between them is essential in computer programming. Decimal numbers use the base 10 system, while binary numbers use the base 2 system. This article will delve into the details of decimal to binary conversion.

### Understanding how to convert from decimal to binary

is a fundamental concept in computer programming. The decimal number system is based on powers of ten, where each digit has a value 10 times higher than the one in the column to its right. In contrast, the binary number system is a base 2 system where each digit has a value twice that of the digit to the right. The two possible digits in binary are 0 and 1.

One technique to convert a decimal number to binary is to divide repeatedly by two until the quotients are 0. Take the remainder of each division starting from the last quotient to the first, and you will get the binary equivalent. For illustration, let’s convert the decimal number 23 to binary.

23 divided by 2 gives a quotient of 11 and a remainder of 1. Half of 11 is 5, with a remainder of 1. Half of 5 is 2 with a remainder of 1. Half of 2 is 1 with a remainder of 0. And finally, half of 1 is 0 with a remainder of 1. Writing down the remainders in reverse, we get the binary equivalent of 23, which is 10111.

Another technique to convert a decimal number to binary is to use the power of 2. For instance, the binary equivalent of 23 is 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1* 2^0. Simplifying this equation gives 16 + 0 + 4 + 2 + 1 = 23. Writing the coefficients of 1’s and 0’s, we get the binary equivalent of 23 as 10111.

It’s noteworthy that there are also tools readily available to convert a decimal number to binary. Several programming languages have inbuilt decimal to binary conversion functions. You can also use online decimal to binary converter tools whereby the user inputs the decimal number and the output is the binary equivalent.

understanding how to convert from decimal to binary is essential in computer programming and computer engineering. Learning and mastering the skill of converting between decimal and binary is critical for conducting computer system analysis, developing computer programs, and other computer technology applications. The techniques presented, dividing by two and using the power of two, are some of the common methods used to convert from decimal to binary. By grasping these techniques, you can convert decimal numbers to binary manually. However, with readily available conversion tools, like online decimal to binary converters, you can easily and quickly get the binary equivalent of any decimal number.