Decimal to Binary Converter
To use this decimal to binary converter tool, you should type a decimal value like 308 into the left field below, and then hit the Convert button. This way you can convert up to 19 decimal characters (max. value of 9223372036854775807) to binary value.
Decimal to binary conversion result in base numbers
The decimal numeral system is the most commonly used and the standard system in daily life. It uses the number 10 as its base (radix). Therefore, it has 10 symbols: The numbers from 0 to 9; namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
As one of the oldest known numeral systems, the decimal numeral system has been used by many ancient civilizations. The difficulty of representing very large numbers in the decimal system was overcome by the Hindu–Arabic numeral system. The Hindu-Arabic numeral system gives positions to the digits in a number and this method works by using powers of the base 10; digits are raised to the nth power, in accordance with their position.
For instance, take the number 2345.67 in the decimal system:
- The digit 5 is in the position of ones (100, which equals 1),
- 4 is in the position of tens (101)
- 3 is in the position of hundreds (102)
- 2 is in the position of thousands (103)
- Meanwhile, the digit 6 after the decimal point is in the tenths (1/10, which is 10-1) and 7 is in the hundredths (1/100, which is 10-2) position
- Thus, the number 2345.67 can also be represented as follows: (2 * 103) + (3 * 102) + (4 * 101) + (6 * 10-1) + (7 * 10-2)
The binary numeral system uses the number 2 as its base (radix). As a base-2 numeral system, it consists of only two numbers: 0 and 1.
While it has been applied in ancient Egypt, China and India for different purposes, the binary system has become the language of electronics and computers in the modern world. This is the most efficient system to detect an electric signal’s off (0) and on (1) state. It is also the basis for binary code that is used to compose data in computer-based machines. Even the digital text that you are reading right now consists of binary numbers.
Reading a binary number is easier than it looks: This is a positional system; therefore, every digit in a binary number is raised to the powers of 2, starting from the rightmost with 20. In the binary system, each binary digit refers to 1 bit.
How to Read a Binary Number
In order to convert binary to decimal, basic knowledge on how to read a binary number might help. As mentioned above, in the positional system of binary, each bit (binary digit) is a power of 2. This means that every binary number could be represented as powers of 2, with the rightmost one being in the position of 20
Example: The binary number (1010)2 can also be written as follows:
(1 * 23) + (0 * 22) + (1 * 21) + (0 * 20)
Decimal to binary conversion examples
- (51)10 = (110011)2
- (217)10 = (11011001)2
- (8023)10 = (1111101010111)2
Related converters: Binary To Decimal Converter
Decimal Binary Conversion Chart Table