Binary number is a number written using only two digits, generally 1 and 0. Binary numbers are especially important in the modern world, where computers use them for most basic functions.
Loading the player...Computer circuit board
The binary number system is also called base 2. It can be contrasted with the more familiar decimal system, or base 10, commonly used in everyday life. The decimal system uses 10 digits—0 through 9.
Places.
In the decimal system, large numbers are represented using places. In the decimal number 213, for example, 2 is in the hundreds place, 1 is in the tens place, and 3 is in the ones place. The number 213 thus stands for 2 hundreds, 1 ten, and 3 ones. Each place represents a power of 10—that is, 10 multiplied by itself a certain number of times (see Power ). The number 1 is 10 to the zero power, written as 100; 101 is 10; 102 is 100, and so on.
Binary numbers work the same way, except that the places represent powers of 2, rather than 10. So, instead of ones (100), tens (101), hundreds (102), and thousands (103) places and so on, binary numbers have ones (20), twos (21), fours (22), eights (23), and sixteens (24) places and so on. For example, the binary number 101 stands for 1 four, 0 twos, and 1 one. The binary number 101 thus equals the decimal number 5.
In arithmetic.
Addition and multiplication work the same in binary as in the decimal system. But because there are only two symbols in binary, the rules may appear quite simple. For example, the rules for addition in binary are as follows:
The last result may look strange. But the number 10 in binary is the same as the number 2 in decimals. Using these rules, we can add the binary numbers 101 and 11 as follows:
When multiplying in the binary system:
History.
Gottfried Wilhelm Leibniz, a German philosopher and mathematician, developed and promoted the binary system in the late 1600’s. However, binary only reached widespread importance with the invention of electronic computers, which began in the 1930’s and 1940’s. In a computer, circuits can be switched “on” or “off” to let an electric current pass through or not. These “on” and “off” states can physically simulate the 1’s and 0’s of binary arithmetic. Modern computers can perform huge numbers of binary calculations at extremely fast speeds, processing vast amounts of data.
See also Computer (Representing computer data) ; Digital technology .
