Binary notation

Binary Notation is a system of numerical notation that is based on the binary number system, which uses only two symbols: typically 0 (zero) and 1 (one). The binary system is used internally by almost all modern computers and computer-based devices because it is straightforward to implement with digital electronic circuitry using logic gates. The most basic unit of information in computing and digital communications, the bit, is a binary digit.

History

The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. However, binary systems similar to binary notation have been used in ancient Egypt, China, and India.

Representation

In binary notation, numbers are represented using two symbols: 0 and 1. Each digit in a binary number represents a power of 2. The rightmost digit represents 2^0 (1), the next digit to the left represents 2^1 (2), the next represents 2^2 (4), and so on.

Conversion

Conversion from binary to decimal and vice versa is a basic operation in computing. To convert a binary number to decimal, each binary digit is multiplied by an increasing power of 2 starting from the rightmost digit, and the results are summed. To convert a decimal number to binary, the number is divided by 2, and the remainder is the least significant bit; this process is repeated with the quotient, until the quotient is 0.

Applications

Binary notation is used in nearly all modern computing systems. It is used to represent instructions, data, and hardware states. It is also used in mathematical and logical operations.

See also

• Binary code
• Binary numeral system
• Bit
• Boolean algebra