Reviewing Binary

It's All 1s and 0s

These days, our lives are extremely data-rich: everything we see and hear from a computer is made up of data. For example, today on my way to work, I was listening to music while looking at my Twitter feed and and a picture of my friend’s cat on Instagram. All of these things — music, text, and photos — are essentially just series of ones and zeros. At the very basic level, this is what all digital information consists of.

So how do ones and zeros become music, social media messages, or images of cats? To begin to answer this question, I will take you on a short tour of the history and meaning behind data and digital media to give you an idea of how we have come this far with mere ones and zeros.

A computer’s job

Computers were built for the purpose of processing data to turn it into information. Information is closely related to data; the main difference is that data is a formalised representation of something which, when given context or when analysed, becomes information. So data is a more abstract term than information.

In this course we are mainly concerned with how data is represented by computers, and not with how computers process and create information. This is an important distinction, as the aim of this course is to help you understand the formalisations and codes that computers use to bring data to life. Essentially, you will learn to understand things from the point of view of a computer — things that you see, hear, and take for granted in your everyday life. This knowledge is very relevant to many aspects of computer science theory.

A computer is designed to do a number of things with data: + Receive data + Store data + Manipulate data + Present data

This all happens internally within the computer. So how do computers receive, store, manipulate, and present data just by using electricity? In our course How Computers Work we explain that computers are made up of a number of switches that can be either on or off, and these states correspond to the binary representation 1 (on) and 0 (off). Electrical current flows through the switches, and if you add more switches, you get more ones and zeros. Here is an example of how this works:

Each 1 (on) or 0 (off) state in a single switch is called a bit, which is the smallest piece of data a computer can store. If you use more switches, you get more bits; with more bits you can represent more complex data like the music, text, and image I talked about earlier. Billions of switches fit onto a single circuit board, and computers bring data to life by working with these bits.

During this course, we will look at the processes computers use to turn these bits into things you can see and hear. The first step is to understand how information is converted from a physical format into a digital one that can be represented by bits. This process of conversion is called digitisation.

Digitisation

To understand digitisation, let’s look at how much technology has developed in the last 25 years. Multimedia technology and the internet have transformed us into a digital culture. For example, this is technology that was popular 25 years ago in 1993, compared with current technology:

Today, most forms of mass media, television, recorded music, and film are produced and distributed digitally, and they are now converging with the internet and World Wide Web to create the digital mediascape we experience every day. Here are a few interesting facts about the digitisation of media:

Nearly all music humans have ever recorded has now been digitised
In 2011, Amazon started selling more digital books than print books
In 1986, 99.2% of the world’s information storage capacity was analogue; 21 years later, in 2007, 94% was digital

In the pictures above, the examples of popular technology from 1993 are analogue, and the examples from 2018 are digital. We will go through the differences between analogue and digital in more detail later on. For now, to explain how digitisation has progressed from 1993 to today, I’ll give you a quick overview of analogue and digital technology.

Analogue electronics, like the examples from 1993, use analogue signals. You can imagine analogue signals as similar to the temperature line on a mercury thermometer: the line changes continuously to indicate the temperature.

Like this mercury thermometer line, analogue signals can take a continuous range of values to represent data, and this range can be visualised. On the other hand, a digital thermometer shows values in discontinuous steps, for example tenths of a degree.

Old broadcast televisions serve as another example: these TVs use a signal with a continuously variable wave to represent sounds and visuals.

Because variations in these waves are so small, the wave forms can be interrupted by interference, which causes things like static sound and snow visuals. To reduce interference, computers can convert the waves into ones and zeros (or bits) as single pieces of data. Using bits instead of wave forms reduces the effects of interference and results in better quality sound and visuals. Computers therefore represent media in numerical format, and this has had a large, and growing, impact on what we see and hear in our everyday lives.

This week we will dive deeper into the mathematics and basic computing processes underlying media computation and data representation.

Activity: everyday data

Now you have seen some examples of how data is represented, think about the data that is brought to life for you every day through your phone, laptop or desktop computer, and all the other computers around you, like digital displays on your daily train ride, your smart TV at home, or the digital radio in your car.

Pick one or two examples of data you see represented in your everyday life, and share them in the comment.

Binary

Number systems

The number system we normally use is the base 10 or decimal system, also called denary. This system is based on the number ten, which is a very important number for us humans. Because we have ten fingers, when someone tells us: “I have ten cookies”, we will immediately assume this amount of cookies because we are used to counting with ten fingers:

However, some cartoon characters have only eight fingers. If we told them that we had ten cookies, they might think that we had this many cookies:

These cartoon characters would probably have their own number system that isn’t based on the number ten, but the number of fingers they have: eight. We would call this an octal number system, or base 8. This is how they might count:

What number system would fish have?

If you guessed base 2 or binary, you’re correct! Because Nemo and Dory are fish and have two main fins, if we told them we have ten cookies, this is what they might think:

And this is how they might count the cookies:

This is similar to a computer’s number system because, as you learned in the previous step, computers are made up of billions of switches, and switches only have two states: on and off.

Here’s a table summarising how the binary number system compares to the decimal system when looking at powers of two. The binary numbers look like they are very large quantities, but 100000000 in binary is the same quantity as 256 in denary, it just looks longer.

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