Data and Data Representation

Why computers use binary

Everything a computer stores, whether a message, a photograph or a song, is held as binary: long strings of just two digits, 0 and 1. Computers use binary because their circuits have two steady states, on and off, which map neatly onto 1 and 0. A single one of these digits is a bit, and eight bits together make a byte. From those simple building blocks a computer represents numbers, text, images and sound. This module covers why binary is used, how to read it, how much data the units hold, and how different kinds of data are turned into binary.

Data words

Learn these terms before working with data. They are the words every data-representation answer needs.

Match each data term to its meaning

Binary against denary

Two number systems matter here. Denary is the one people count in every day; binary is the one computers use. The difference is simply how many digits each one has.

How many bits in a byte?

How many bits are there in one byte?

• Eight
• Two
• Four
• Ten

Reading binary place values

To turn a binary number into denary, give each digit a place value. Reading from the right, the places double: one, two, four, eight, and so on. Write the place values above the digits, then add up only the place values that sit above a 1. So for the four-digit number 1010, the places are eight, four, two and one. There is a 1 above the eight and a 1 above the two, so the total is eight plus two, which is ten. Line the places up, add where there is a 1, and the conversion is quick and reliable.

Pick the true data facts

Select every true statement about data and how computers store it.

• Computers store all data as binary
• A bit is a 0 or a 1
• A byte is made of eight bits
• Binary uses the digits 0 to 9
• Computers cannot store images

Order the units of storage

Put these units of data storage in order from the smallest to the largest.

• bit
• byte
• kilobyte
• megabyte
• gigabyte

Complete the data facts

A single 0 or 1 is called a _____. Eight of them make one _____. The number system computers use is _____. A single dot of colour in an image is a _____.

Turning a photo into numbers

Think about how a photograph becomes binary. The image is split into a grid of tiny squares called pixels, and each pixel is given a number that stands for its colour. That number is stored as binary, so the whole picture becomes a long stream of ones and zeros. A picture with more pixels, or more possible colours per pixel, needs more bits, so its file is larger. Sound is handled in a related way: the wave is measured many times a second, and each measurement, called a sample, is stored as binary too. In every case the same idea holds, that real things are turned into numbers and the numbers are stored in binary.

Spot what is stored as binary

Tap the TWO things that a computer represents using binary.

• a digital photograph
• a recorded song
• the taste of an apple
• the smell of fresh coffee

Work out the denary value

Using the place values 8, 4, 2 and 1, what is the binary number 1010 as a denary number? Add the place values that sit above a 1.

Represent each kind of data

Read each situation and choose the best answer.

• A computer needs to store a photograph. In what form does it store it?
• A computer needs to store a sound. How does it do this?
• The binary number 1000 uses the place values 8, 4, 2 and 1. What is it in denary?

Build a data point

Choose the word for each gap to complete one clear point about how computers store data.

Explain data and data representation

A friend cannot see how a photograph could possibly be just numbers. Using what you have learned, explain how computers represent data.

• Explain why computers use binary
• Explain what a bit and a byte are
• Explain how to turn a small binary number into denary
• Explain how images and sound are represented as binary