Data representation flashcards

Data representation covers how computers store and process all types of data using binary, a number system with only two digits: 0 and 1. Students must understand how to convert between binary, denary (base 10) and hexadecimal (base 16), and how to perform binary addition. You also need to know how text is encoded using systems such as ASCII and Unicode, how images are stored as pixels with colour depth and resolution, and how sound is digitised through sampling. Units of data storage from bits and bytes up to terabytes are essential, as is understanding how file size is calculated. The concept of overflow, where a result is too large to store in a given number of bits, is also important. Understanding why hexadecimal is used as a shorthand for binary is a key linking idea throughout the topic.

1. Card 1

   What is a bit and what values can it hold?

   A bit is the smallest unit of data in a computer. It can hold only one of two values: 0 or 1.

2. Card 2

   How many bits are in a byte?

   There are 8 bits in one byte. A byte can represent 256 different values (2 to the power of 8).

3. Card 3

   Convert the binary number 10110011 to denary.

   Using place values (128,64,32,16,8,4,2,1): 128+32+16+2+1 = 179. The denary value is 179.

4. Card 4

   What is hexadecimal and why is it used in computing?

   Hexadecimal is base 16, using digits 0-9 and A-F. It is used because it represents binary more compactly, making long binary strings easier for humans to read and write.

5. Card 5

   Convert the hexadecimal value 2F to denary.

   2 x 16 = 32, then add 15 (F = 15). 32 + 15 = 47. So 2F in hexadecimal equals 47 in denary.

6. Card 6

   What is ASCII and what is its limitation?

   ASCII assigns a unique 7-bit binary code to each character. Its limitation is that it only covers 128 characters, so it cannot represent most world languages or symbols.

7. Card 7

   How does Unicode improve on ASCII?

   Unicode uses more bits per character (up to 32), allowing over a million unique characters. This means it can represent scripts and symbols from virtually every language in the world.

8. Card 8

   What is a pixel and how does it relate to image storage?

   A pixel is the smallest single point of colour in a digital image. Images are stored as a grid of pixels, and each pixel's colour is represented by a binary value.

9. Card 9

   What is colour depth in digital images?

   Colour depth is the number of bits used to represent the colour of each pixel. A greater colour depth means more possible colours but also a larger file size.

10. Card 10

    How is the file size of an image calculated?

    Image file size = width in pixels x height in pixels x colour depth (in bits). The result is in bits; divide by 8 for bytes.

11. Card 11

    What is sampling rate in digital sound?

    Sampling rate is how many times per second the amplitude of a sound wave is measured. A higher rate produces better quality audio but creates a larger file size.

12. Card 12

    What is overflow in binary arithmetic?

    Overflow occurs when the result of a binary calculation is too large to fit in the available number of bits, causing data to be lost and an incorrect result to be stored.

• Students often confuse colour depth with the number of colours, forgetting that the number of colours is 2 to the power of the colour depth, not the colour depth value itself.
• When converting binary to denary, students frequently add up place values incorrectly by starting from the wrong end, assigning 1 to the leftmost bit instead of the rightmost.
• Many students think that Unicode and ASCII are completely different systems, when in fact Unicode was designed to be backward compatible with ASCII for the first 128 characters.

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