A binary number is a number expressed in the base-2 numeral system, which uses only two digits: 0 and 1. This is in contrast to the decimal (base-10) numeral system that we use in everyday life, which uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

In the binary system, each digit represents a power of 2, starting with $2^0$ (which is equal to 1) and increasing by a factor of 2 for each successive digit. For example, the binary number 1011 represents:

Binary numbers are commonly used in computer science and digital electronics because they can be easily represented using electronic switches that are either on or off (i.e., 1 or 0). This makes them ideal for representing digital data, such as the instructions that a computer executes or the pixels in a digital image.

In addition to binary, there are other numeral systems that use different bases, such as octal (base-8) and hexadecimal (base-16). These systems are also commonly used in computer science and digital electronics because they can be easily converted to and from binary.

Examples

The following table shows the decimal, binary representations of the numbers 0 through 15:

References

• Binary Number Wikipedia
• Decimal Number
• Hexadecimal Number
• Octal Number