Red and amber points, pupil by pupil

Units of data

A bit is one 0 or 1. A nibble is 4 bits. A byte is 8 bits.

After the byte, each unit is 1024 times bigger than the one before.

1024 is used because it is a power of 2: 2¹⁰ = 1024. Computers count in powers of 2.

Try the toy: type 1 and choose GiB. Read the MiB and KiB rows in the table. How many times did you multiply by 1024 to reach KiB?

There is something to try for this step in the IGCSE library.

Converting between units

Going to a smaller unit: multiply (× 1024, or × 8 from bytes to bits).

Going to a bigger unit: divide (÷ 1024, or ÷ 8 from bits to bytes).

Move one unit at a time and write each step. It is slower but it avoids mistakes.

Calculating image file size

Every pixel needs the same number of bits: the colour depth.

So file size in bits = number of pixels × colour depth. Number of pixels = width × height.

Then divide by 8 for bytes, by 1024 for KiB, and by 1024 again for MiB.

Real files are a little bigger, because they also store extra data such as the width and height.

Calculating sound file size

Each second you take (sample rate) samples. Each sample uses (sample resolution) bits.

So file size in bits = sample rate × sample resolution × length in seconds.

Then divide by 8 for bytes and by 1024 for KiB or MiB, as for images.

This is for one channel (mono). Change minutes into seconds first.

Why we compress files

Compression makes a file smaller, so it uses fewer bits.

Smaller files use less storage space on a device or server.

Smaller files need less bandwidth. Bandwidth is how much data a connection can carry each second.

So smaller files are sent faster: quicker downloads, quicker uploads, and less buffering when streaming.

Many services set a size limit. An email attachment limit of 25 MB is a real example.

Lossy compression

Lossy compression removes data permanently. You can never get the original back.

It removes detail people are unlikely to notice, such as sounds humans cannot hear or tiny colour differences.

Ways to do it: lower the image resolution or colour depth, or lower the sample rate or sample resolution.

Examples: JPEG for photos, MP3 for music, and most video streaming.

It gives a much smaller file than lossless, but quality is lower.

Lossless compression

Lossless compression makes the file smaller without losing any data.

When the file is decompressed, it is exactly the same as the original, bit for bit.

It finds patterns and repeats in the data and stores them in a shorter way.

Use it when every bit matters: text, program files, spreadsheets, medical scans.

The file is not made as small as with lossy compression.

Run-length encoding (RLE)

Run-length encoding (RLE) is a lossless method. A run is a group of the same value in a row.

RLE stores each run as two values: how many, then which value.

It works well when data has long runs, such as simple images with big areas of one colour.

Try the toy: press All one colour, then press Stripes so every pixel is different from the next. Compare the sizes before and after RLE.

There is something to try for this step in the IGCSE library.

RLE: working out the saving

To judge compression, compare the size before and after.

RLE only helps when runs are long. If values change all the time, RLE can make the file bigger.

That is why RLE suits simple graphics and icons, but not photographs.

The CPU and the microprocessor

The CPU (central processing unit) is the part of the computer that processes instructions and data. It carries out the instructions of every program.

It does this by fetching an instruction from memory, decoding it, then executing it. Then it repeats, billions of times a second.

A microprocessor is a CPU built as an integrated circuit on a single chip. An integrated circuit is a whole electronic circuit made on one small piece of silicon.

Von Neumann architecture

Most computers follow the von Neumann architecture. Its key idea is the stored program: instructions and data are both stored in the same main memory.

The CPU has a control unit (CU). The CU manages the fetch–decode–execute cycle. It decodes instructions and sends control signals to the other parts.

The CPU has an arithmetic logic unit (ALU). The ALU does calculations (such as add and subtract) and logic operations (such as comparing two numbers).

The CPU also has registers: very small, very fast stores inside the CPU. The CPU is joined to memory by three buses (sets of wires).

There is a diagram for this step in the IGCSE library.

The five registers

A register holds one item at a time: an address, an instruction or a piece of data.

An address is the number of a location in memory, like a locker number in a school corridor.

The three buses

The address bus carries addresses from the CPU (the MAR) to memory. It is one-way (unidirectional), because only the CPU chooses addresses.

The data bus carries data and instructions between the CPU (the MDR) and memory. It is two-way (bidirectional), because data is both read and written.

The control bus carries control signals from the control unit, such as 'read', 'write' and the clock signal. It is two-way, because devices also send signals back.

The fetch–decode–execute cycle

Every instruction goes through the same three stages. Learn the fetch stage in order: it is worth most marks.

Fetch: the address in the PC is copied to the MAR, using the address bus. The PC is incremented (1 is added), so it points to the next instruction. The instruction at that address is sent along the data bus to the MDR. It is then copied from the MDR to the CIR.

Decode: the control unit decodes the instruction in the CIR. It works out what the instruction means and what needs to happen.

Execute: the instruction is carried out. The control unit sends signals on the control bus. If there is a calculation, the ALU does it and the result goes in the ACC. Then the cycle starts again.

There is something to try for this step in the IGCSE library.

The instruction set

An instruction set is the list of all the instructions (commands) that a particular CPU can understand and carry out.

Each instruction is a binary code, called machine code. Examples are load, add, store, compare and jump.

The CU decodes instructions using this set. Different CPU families have different instruction sets.

Cores, cache and clock speed

Clock speed is the number of fetch–decode–execute cycles the CPU can do per second, measured in hertz (Hz). A 3.5 GHz CPU has 3,500,000,000 clock ticks per second. Higher clock speed means more instructions per second.

Cache is a small amount of very fast memory inside or next to the CPU. It stores instructions and data that are used often, so the CPU does not have to wait for slower RAM. More cache means fewer slow trips to RAM.

A core is a complete processing unit (with its own ALU, CU and registers). A quad-core CPU has four cores, so it can process four instructions at the same time.

Embedded systems

An embedded system is a small computer system built inside a larger device, to do one dedicated job.

It uses a microprocessor (or a microcontroller) and usually runs one fixed program stored in ROM.

A general-purpose computer, like a laptop, can run many different programs and do many jobs.

What a trace table is

A dry run means working through an algorithm by hand, line by line, without a computer.

A trace table records the dry run. It has one column for each variable, and one for the output.

Write a new value in a column only when that variable changes. Move to a new row when the loop goes round again.

Worked dry run

This algorithm reads numbers until the user types -1. A value that only means 'stop' is called a rogue value.

Input data: 12, 7, 20, 9, -1. Follow each row of the table below and check you agree.

Then use the toy. Pick Counting (WHILE), a similar rogue-value loop, and press Step to run it one line at a time.

DECLARE Value : INTEGER
DECLARE Total : INTEGER
DECLARE Count : INTEGER
DECLARE Highest : INTEGER
Total ← 0
Count ← 0
Highest ← 0
INPUT Value
WHILE Value <> -1 DO
  Total ← Total + Value
  Count ← Count + 1
  IF Value > Highest
    THEN
      Highest ← Value
  ENDIF
  INPUT Value
ENDWHILE
OUTPUT Total / Count, " ", Highest

total = 0
count = 0
highest = 0
value = int(input())
while value != -1:
    total = total + value
    count = count + 1
    if value > highest:
        highest = value
    value = int(input())
print(total / count, highest)

There is something to try for this step in the IGCSE library.