Binary Number

lastmod 2018-08-17created 2014-06-122 edits

The binary system (binary) is a number system that uses only two digits. By convention, the symbols 0 and 1 are used, and numbers made up of them are called binary numbers. The binary system was invented by Leibniz. Decimal 1 is 1 in binary, decimal 2 is 10 in binary, and decimal 3 is 11 in binary.

Computers use binary because it makes logic simple to build and suits the characteristics of the components used inside them. Digital signals are basically sequences of binary numbers, and the numbers processed inside a computer are basically binary, so its importance has grown in the modern era where computers are widely used.

How to convert a decimal number with a fractional part to binary

Decimal point is how to convert the binary As shown in the figure above, to convert 0.3 to binary, keep dividing by 2. Then write down the number that appears in the integer place (the remainder).

1. 0.3 / 2 = 0.6 ... 0
2. 0.6 / 2 = 1.2 ... 1
3. 0.2 / 2 = 0.4 ... 0
4. 0.4 / 2 = 0.8 ... 0
5. 0.8 / 2 = 1.6 ... 1

Result: 0.01001 ...

Favorite site

• Wikipedia (en) description of binary numbers
• Practice converting real numbers (integers) with a decimal point between bases ¹

References