Decimal to Binary Converter
Convert any decimal number to its binary representation instantly
Calculation Steps
Explaining Two Number Systems: Decimals and Binary
Decimal number systems are systems that are widely used and common all around us.
Because of the prevalence of computers and digital electronics, the binary number system is also very important. Devices that perform the tasks of conversion from decimal to binary are essential for bridging the gap between how humans can count and how machines perform complex functions. This guide will explain the importance of the two systems, how to convert them from one to the other, and the importance of technology to perform these conversions.
What are the Systems of Decimals, Base 10?
Daily, we employ the decimal system or the base 10 number system.
This is referred to as the base 10 system due to the fact that it employs 10 basic numerals, which are: 0, 1, 2, 3, 4, 5, 6, 7,8, and 9. The decimal system has an important characteristic, which is positional value. For every number, each of its digits has a value determined by its position, which is a power of 10. Consider the digits of the number 345, where we break down each digit to the power of 10:
5 is 5 x 1 = 5 at the (0th power of 10 [ that is, the ones]).
4 is 40 at the (1st power of 10 [ that is, tens]). Because the digit 3 is in the hundreds place (102), the digit has a value of 3 x 100 = 300.
When all the values are added together. We get the number: 300 + 40 + 5 = 345. While humans can get numbers in this positionally intuitive manner, it is less so for digital hardware.
What is the Binary (Base-2) Number System?
The binary system (also called base-2) is the language of computers. It has a digit set of only 0 and 1, called “bits.” Every piece of data in a computer, from a letter to an image to program instructions, is stored and processed as a long sequence of 0s and 1s.
Why Do Computers Use Binary?
Because binary is the only number system that works with a computer’s fundamental building blocks, transistors. A tiny electronic switch can be in one of two states: ON or OFF. The states are represented by 1 (ON) and 0 (OFF). Binary is by far a simpler two-state system, and far more reliable to manufacture, than a decimal system, which would need to switch between ten different states for every digit.
Converting Decimal to Binary manually
Converting numbers from decimal to binary can be done in several ways, but the easiest has to be the Remainder or division method. Just like our converter divides the number by 2 and collects the remainder for each division. You should understand how the converter works, so let us convert 29 Decimal to Binary in each of the steps our converter performs.
Converting 29 Decimal to Binary
Step 1: 29 can be divided by 2, which will result in 14. 1 will be the remainder.
Step 2: 14 can be divided by 2, which will result in 7, and the remainder will be 0.
Step 3: 7 can be divided by 2, which will result in 3, and the remainder will be 1.
Step 4: 3 can be divided by 2, which will result in 1, and the remainder will be 1.
Step 5: Finally, when 1 can be divided by b, which results in 0, and the remainder will be 1.
Step 6: You should have recognised the pattern by now. The process ends when the result of the division is 0.
To finalise the binary number, we read the remainders. The order in which we read the remainders is from the last step to the first step. In this example, we have the remainders: 1,0,1,1. Reversing the order, we get 1 1 1 0 1.
This means the binary representation of the decimal number 29 is 1 1 1 0 1 or 11101.
Decimal to Binary Conversion Chart
Every year, we teach students how to convert decimals to binary to show students the difference in base number communication and using different numeric systems. The first 16 base 10 to base 2 binary numbers are shown in the table below:
Decimal (Base-10) Binary (Base-2)
0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001
10 1010
11 1011
12 1100
13 1101
14 1110
15 1111
Frequently Asked Questions (FAQ)
What is the decimal to binary formula?
1. There is not one mathematical formula, but you can use the process of repeated division by 2, the standard algorithm. If you wished to convert the decimal number N, the process would be: 1. N (floor) 2, 2. If N > 0, then go to 1. Reverse the order of the numbers you first listed in the processed you would end up with the binary equivalent of your decimal N.
How do you represent negative decimal numbers in binary?
Typically, numbers to the left of the decimal are converted using a methodology called Two’s Complement. This would be inverting the actual numbers of the binary number by interchanging 0s and 1s. Once complete, simply add 1. This methodology is simpler in terms of hardware design to use subtraction in a computer.
What are some examples of using this conversion in the real world?
The conversion of decimal to binary is the basis of all digital technologies. Every time you press a character or a key on the keyboard, that character is converted to its binary form, and that may be using ASCII or Unicode. In computer networking, binary values are used as IP addresses, and such addresses are converted to decimal form for easier reading and understanding.
Conclusion
The digital world is built on the binary and decimal systems, and knowing how to switch back and forth is fundamental. Unlike other converters, the tool we built to convert decimal to binary is not meant to only give you an answer. Rather, we designed it to teach you the process of conversion at the same time. Whether you are just curious, a developer, or a student, we hope that this tool helps streamline understanding of this fundamental concept
How easy it is to convert values from one number system to another!
