# Binary Number System

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The binary number system, also known as base-2, is a numeral system that uses only two symbols: typically 0 (zero) and 1 (one). It’s the foundational language of most modern digital and computer systems.

In the decimal system (which we use in our everyday counting), the place values are powers of 10 (1, 10, 100, 1000, etc.). In the binary system, the place values are powers of 2 (1, 2, 4, 8, 16, etc.).

Here’s how you can convert a binary number to decimal: each digit in a binary number represents a power of 2. The rightmost digit represents 2^0, the next represents 2^1, then 2^2, and so on. You multiply each digit by the corresponding power of 2 and add up all those products to get the decimal equivalent.

For example, let’s convert the binary number 1101 to decimal:

12^3 + 12^2 + 02^1 + 12^0 = 8 + 4 + 0 + 1 = 13

So, 1101 in binary is equal to 13 in decimal.

This system of numbering is very efficient for machines because a binary digit, or bit, can only represent one of two values, which can easily correspond to the on or off states of electronic switches. It’s this principle that makes binary so important in computers and digital systems.