## Introduction

A binary number is a number expressed in the base-2 numeral system by using only two symbols: 0 and 1. It is just like counting in decimal except we reach 10 much sooner. We start with 0 then 1 and after which we start with 0 again but already with 1 on the left side (10). This is the language which is used to speak with all computer-based devices. Besides the binary there are also 8-based 16 based representations. This is also the base of Boolean algebra: 0 is False, 1 is True.

## How to convert decimal to binary

Let's consider a decimal number 46 and try to convert it to binary.

46/2 will be 23 and 0 reminder

23/2=11, 1 reminder

11/2=5, 1 reminder

5/2=2, 1 reminder

2/2=1, 0 reminder

2/2= 1

So the representation of 46 in binary will be 101110 from below to above.

## How to convert Binary to decimal

Now let's try to convert 11011001 binary number into decimal.

Order start from right to left and we start count from 0.

11011001

*76543210*

Then we are summing up all numbers multiplied by the 2 power of their order number.

## Memory

Each 1 or 0 in binary number is one bit, so 11011001 is 8 bits which is equal to 1 byte. Bit is the smallest measure. Let's consider English Alphabet (there are 26 letters) we can represent it with 5 digits because 4 will be not enough.

00001

00010

…

01111

11111

With 5 digits we can represent 2^5=32 letters or something.

## Addition

Binary addition works like a decimal addition, but the number can have only zeros and ones as digits, so if the sum exceeds 1, you have to carry 1 to the next bit.

When we add 1 to 1 we will get 10 so we will have 0 and 1 carry. Moreover, we can check that by converting these numbers and our answer into decimal.

10001 = 17

11101 = 29

17 + 29 = 46

101110 = 46

## Multiplication

Binary multiplication is similar to the multiplication of decimal numbers.

Here we can also check the results by converting binary numbers into decimal.

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