Year 7 Computing: Summer Assessment

There are 8 bits in one byte.

The component that carries out the instructions is the CPU, the central processing unit. The component that holds the programs and data in use right now is RAM, which is wiped as soon as the power is switched off.

The int function converts a value into a whole number. It is needed after input because input always hands back text, even when the user typed digits, and text cannot be used in a calculation. Without the conversion, adding one to the answer would either cause an error or join the characters together instead of doing arithmetic.

First I write the place values 128, 64, 32, 16, 8, 4, 2 and 1 above the eight digits. The digits 1 appear in the 128, 32, 16 and 4 columns. Adding those place values gives 128 + 32 + 16 + 4, which is 180. The answer is 180.

Working from the left, 128 does not fit into 73 so I write 0. 64 does fit, so I write 1 and 73 minus 64 leaves 9. 32 and 16 do not fit, so I write 0 and 0. 8 fits, so I write 1 and 9 minus 8 leaves 1. 4 and 2 do not fit, so I write 0 and 0. 1 fits, so I write 1 and nothing is left. The answer is 01001001, and checking it gives 64 + 8 + 1, which is 73.

The reason is electrical. Everything inside a computer is built from circuits that are either on or off, and those two states are extremely easy to tell apart even when the components are tiny and the signal is weak. Binary needs only two digits, so 1 can mean on and 0 can mean off. Building circuits that could reliably tell ten different voltage levels apart would be far more expensive and far more likely to make mistakes, so two states are used and everything else is built up from them.

The CPU fetches the next instruction from memory, then decodes it to work out what that instruction actually means, then executes it by carrying out the work, which might be a calculation, a comparison or moving data. It then goes straight back to the beginning and fetches the next one. This cycle never stops while the computer is on, and a processor running at 3 GHz goes round it three billion times a second.

The problem is that input always hands back text, so tickets holds the characters typed rather than a number. In Python, multiplying a piece of text by 3 does not do arithmetic, it repeats the text three times, which is exactly what the student is seeing on the screen. The fix is to convert the input into a whole number first, by writing tickets = int(input('How many tickets? ')), after which total = tickets * 3 does real arithmetic and gives the cost.

The program is mark = int(input('Enter your mark: ')). Then if mark >= 50: print('Pass'). Then else: print('Fail'). The int function is needed because input gives text and the comparison needs a number. The two lines under the if and the else must be indented by four spaces, and there must be a colon at the end of both the if line and the else line.

A bitmap image is stored as a grid of pixels, with the colour of every single pixel recorded, while a vector image is stored as a list of instructions for drawing shapes, such as a circle at a certain position with a certain radius and fill colour. The second difference follows from the first. Enlarging a bitmap makes it blocky, because there is no extra detail to show and the existing pixels simply get bigger, whereas a vector stays perfectly sharp at any size because the shapes are worked out and drawn again each time. A photograph should be stored as a bitmap, because it is full of irregular detail and slight colour changes that could not sensibly be described as a set of shapes.

The first thing is simplicity. A logo has to be recognisable at sixteen pixels across on a browser tab as well as a metre wide on a banner, and a complicated design turns into a smudge the moment it is made small. The second thing is that it should work in a single colour. Logos end up printed cheaply, stamped, engraved or photocopied, and a design that only reads when every colour is present fails completely in all of those situations. Testing a logo small and in black and white early on saves redesigning it later.

A photograph is stored as a grid of tiny squares called pixels, and the colour of each pixel is recorded as a binary number. The computer also stores the width and height so that it knows how to arrange the pixels back into a picture. Resolution means how many pixels the image contains, so a photograph taken at a higher resolution simply has more of them. Since every single pixel needs its own binary number to record its colour, doubling the number of pixels doubles the number of values stored, and the file gets bigger. That is why a higher quality photograph always takes up more space.

Everything a computer stores is stored as binary numbers, so both files are really just very long lists of 1s and 0s. Sound is a wave, so the phone measures the height of that wave thousands of times every second, which is called sampling, and each measurement is written down as a number. CD quality takes 44,100 measurements every second. A photograph is a grid of pixels, and the colour of each pixel is also written down as a number, so the picture becomes a long list of colour values. In both cases better quality means more numbers. Taking more samples every second gives a recording that follows the original wave more closely, and using more pixels or more bits for each pixel colour gives a sharper picture with more shades, but each of those choices means more values to store and so a bigger file.