## Binary Data

# Introduction

As computers rely on electronics to process data, they are restricted, at a fundamental level, by the nature of electronics. Thus, all data that is processed, is at the level of electrical signals: signal, or no signal; abstracted to 1 and 0, or true and false. Perhaps you have seen, in movies or imagery, streams of 1's and 0's, such as 10100111110111010101101 . This is referred to as Binary data. The word "binary" means "composed of two things", and in this case the two things are the states "1" and "0".

# Number Systems

## Decimal

In our day-to-day life, we make use of the Base 10 numbering system called Decimal. Base 10 makes use of ten different digits, 0 1 2 3 4 5 6 7 8 9, which is why it is referred to as base 10. In addition, each digit's position is multiplied by 10 to the power of that position, where the right-most number is position 0, then the digit to its left is position 1, and so on.

So, for example, the number **1432" can be expressed as follows:

**1432** (base 10) = (**1** * 10^3) + (**4** * 10^2) + (**3** * 10^1) + (**2** * 10^0)
**1432** (base 10) = (1000) + (400) + (30) + (2)
**1432** (base 10) = 1432 (base 10)

## Binary

The Binary number system works the same way as the Decimal number system, except using Base 2. Which means it only makes use of two digits: 0, and 1. In addition, each digit's position is multiplied by 2 raised to the power of it's position, just as with Base 10.

Thus, "1101" in Binary can be expressed as follows:

**1101** (base 2) = (**1** * 2^3) + (**1** * 2^2) + (**0** * 2^1) + (**1** * 2^0)
**1101** (base 2) = (8) + (4) + (0) + (1)
**1101** (base 2) = 13 (base 10)

## Other

There are many different numbering systems, such as Trinary (Base 3), Hexadecimal (Base 16) or even Base 64, which is often used for encoding large chunks of data.

# Converting to Binary

Converting from Decimal to Binary is quite simple. Here is a video tutorial to show you the procedure:

If you didn't pick up how I was converting Binary to Decimal previously, here is another nice video tutorial for the conversion from Binary to Decimal:

# Exercises:

- Convert 50 (base 10) into Binary.
- Convert 1111 (base 2) into Decimal.
- Convert your age into Binary.
- (Self study) What is one common use of Hexadecimal?

Check your work using this online calculator: http://web2.0calc.com/#p