The decimal and binary number systems are the world’s most commonly used number systems right now.
The decimal system, also known as the base-10 system, is the system we use in our daily lives. It employees ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. However, the binary system, also known as the base-2 system, utilizes only two figures (0 and 1) to represent numbers.
Learning how to transform from and to the decimal and binary systems are important for various reasons. For instance, computers utilize the binary system to represent data, so computer engineers must be competent in changing within the two systems.
Furthermore, comprehending how to convert within the two systems can helpful to solve math questions including large numbers.
This article will go through the formula for transforming decimal to binary, provide a conversion table, and give examples of decimal to binary conversion.
Formula for Converting Decimal to Binary
The procedure of converting a decimal number to a binary number is done manually using the following steps:
Divide the decimal number by 2, and account the quotient and the remainder.
Divide the quotient (only) found in the previous step by 2, and document the quotient and the remainder.
Reiterate the prior steps until the quotient is similar to 0.
The binary equivalent of the decimal number is acquired by reversing the sequence of the remainders received in the last steps.
This might sound complex, so here is an example to portray this method:
Let’s change the decimal number 75 to binary.
75 / 2 = 37 R 1
37 / 2 = 18 R 1
18 / 2 = 9 R 0
9 / 2 = 4 R 1
4 / 2 = 2 R 0
2 / 2 = 1 R 0
1 / 2 = 0 R 1
The binary equal of 75 is 1001011, which is gained by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table depicting the decimal and binary equivalents of common numbers:
Decimal | Binary |
0 | 0 |
1 | 1 |
2 | 10 |
3 | 11 |
4 | 100 |
5 | 101 |
6 | 110 |
7 | 111 |
8 | 1000 |
9 | 1001 |
10 | 1010 |
Examples of Decimal to Binary Conversion
Here are some examples of decimal to binary conversion utilizing the steps talked about earlier:
Example 1: Change the decimal number 25 to binary.
25 / 2 = 12 R 1
12 / 2 = 6 R 0
6 / 2 = 3 R 0
3 / 2 = 1 R 1
1 / 2 = 0 R 1
The binary equivalent of 25 is 11001, which is obtained by reversing the series of remainders (1, 1, 0, 0, 1).
Example 2: Convert the decimal number 128 to binary.
128 / 2 = 64 R 0
64 / 2 = 32 R 0
32 / 2 = 16 R 0
16 / 2 = 8 R 0
8 / 2 = 4 R 0
4 / 2 = 2 R 0
2 / 2 = 1 R 0
1 / 2 = 0 R 1
The binary equal of 128 is 10000000, which is obtained by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Even though the steps described prior provide a way to manually change decimal to binary, it can be tedious and error-prone for large numbers. Fortunately, other ways can be employed to rapidly and effortlessly convert decimals to binary.
For instance, you could use the incorporated features in a calculator or a spreadsheet program to change decimals to binary. You can also use web tools for instance binary converters, that allow you to type a decimal number, and the converter will spontaneously generate the equivalent binary number.
It is worth pointing out that the binary system has handful of constraints contrast to the decimal system.
For instance, the binary system fails to portray fractions, so it is only fit for representing whole numbers.
The binary system additionally requires more digits to illustrate a number than the decimal system. For instance, the decimal number 100 can be represented by the binary number 1100100, that has six digits. The extended string of 0s and 1s can be inclined to typing errors and reading errors.
Concluding Thoughts on Decimal to Binary
Regardless these restrictions, the binary system has some merits with the decimal system. For example, the binary system is lot easier than the decimal system, as it just uses two digits. This simpleness makes it simpler to conduct mathematical functions in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is further suited to depict information in digital systems, such as computers, as it can effortlessly be depicted using electrical signals. As a result, understanding how to transform between the decimal and binary systems is essential for computer programmers and for unraveling mathematical questions involving huge numbers.
Even though the method of converting decimal to binary can be tedious and prone with error when worked on manually, there are applications that can quickly change within the two systems.
