## What is the binary number system?

A binary number is a number that we express in a two-digit system or a binary numeric system. This system is described in two integer symbols: in “0” and “1”. That number refers to one bit. Due to its simplicity and ease of application, it is used today in digital electrical circuits. Today, the binary system is used daily in modern computers and similar devices.

## History

Long before the binary system was in use in modern times. Which was in use by ancient Egypt, China, and India.

Horus-eye fractions are a binary counting system for quantities of liquid, grain, or other measures, in which the hekat was expressed in fractions of 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64. The method used by the ancient Egyptians for multiplication is also very similar to binary numbers. They used this method to multiply one number by another using a sequence of steps in which the result is either doubled or has the first number added to it again. They used this method in Egypt as early as 1650 BC.

## Binary counting

Counting in a binary system is similar to counting in other systems. It starts with a single digit. The counting goes through each symbol in descending order. To make the counting in the binary system clearer, we will explain the counting in the decimal.

## Counting in decimal

To make the counting in the binary system clearer, we will explain the counting in the decimal. The decimal counting system uses ten symbols from 0 to 9. Counting begins with the incremental substitution of the last digit (right digit), otherwise called the first digit. When all positions are used with all ten symbols, the right digit is restarted to 0, and the left digit increases by one (overflow).

Counting example: 001, 002, 003, 004, …, 009 (then you reset right digit to 0 and left increase by 1) and will be: 010, 011, 012, 013, 014.

## Counting in binary

It follows the same procedure, except that it has only two symbols 0, 1. when the digit reaches 1 in binary, it automatically restarts to 0, and the left number is increased by 1.

Example

0000 | 0 | 1000 | 8 |

0001 | 1 | 1001 | 9 |

0010 | 2 | 1010 | 10 |

0011 | 3 | 1011 | 11 |

0100 | 4 | 1100 | 12 |

0101 | 5 | 1101 | 13 |

0110 | 6 | 1110 | 14 |

0111 | 7 | 1111 | 15 |

## Addition

The most straightforward operation in a binary system is addition. Adding two digits is relatively easy, using this switching method:

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 0

## What is the hexadecimal counting system?

In mathematics and computing, a Hexadecimal numeric system represents numbers using a base of 16 symbols. The most commonly used symbols are from 0 to 9, which represent values from 0 to 9. The other five characters are from A – F, representing values from 10 to 15.

## Example of converting Hexadecimal

**111110001010100000010101 _{2} = F8A815_{16}**

_{ Convert each group of 4 bits (nibble) to its equivalent hexadecimal value. Combine all the results to get the hexadecimal value.}

_{1111} | _{1000} | _{1010} | _{1000} | _{0001} | _{0101} | _{Binary} |

_{F} | _{8} | _{A} | _{8} | _{1} | _{5} | _{Hexadecimal} |