Data

Unfinished. These only include Year 10 content, sorry.

Binary

Base 2, e.g. 1001 1101

Denary

Base 10, e.g. 24

Hexadecimal

Base 16, e.g. 5F (one digit per nibble), used for MAC addresses and colours

Bits and bytes

one binary digit, 8 binary digits (bits)

1000 storage units

KB (kilobyte), MB (megabyte), GB (gigabyte), TB (terabyte)

1024 storage units

KiB (kibibyte), MiB (mebibyte), GiB (gibibyte), TiB (tebibyte)

Binary arithmetic

Operations fundamental to all computer calculations

ASCII

American Standard Code for Information Interchange - 7 bit character set

A is at 65, a is at 97 - 32 between upper and lower case

Solutions to ASCII limitations

Extended ASCII (8 bit ASCII), unicode

Logical left shift

Unsigned integers

Move MSB left, move other digits, fill space with 0s

Can lead to overflow

Arithmetic left shift

Signed integers

Same as logical left shift

Can lead to sign-flipping

Logical right shift

Unsigned integers

Move LSB right, move other digits, fill space with 0s

Can lead to loss of precision

Arithmetic right shift

Signed integers

Move LSB right, move other digits but MSB is maintained, fill space with MSB

Can lead to loss of precision

Overflow responses

• Crash and report overflow error

• Truncate the number

• Wrap the number back around to 0

Two’s complement

Used for signed integers - MSB is a negative number

Conversion: starting from the right, copy out every number up to and including the first 1, flip every number after that

Bitmap

Representing an image as rows and columns of pixels (picture elements)

Qualities of a bitmap

Resolution = number of pixels in an image

Colour depth = bits used to store colour

Metadata = data about the image stored along with it

Image file size calculation

File size in bits = width x height x colour depth

Bitmap trade-offs

More colours than available in colour depth —> similar colours merged

More bits for colour depth than needed —> takes up unnecessary storage space

Analogue data

Data that is continually changing, occurs in nature - continuously variable

Must be converted by and ADC into a digital format to be stored on a digital device

Digital data

Made up of discrete binary values - mapped across entire sample interval

Must be converted into analogue to be played aloud using DAC

ADC conversion

• Sampling - taking a snapshot of the analogue signal at one point in time

• Quantisation - mapping the snapshot onto a binary value

Sound wave graph keywords

Sound wave = the whole wave

Amplitude = the wave’s value at a given time

Bit depth = bits needed to represent the range of values

Bit rate = bits per second

y-axis = binary values

x-axis = time values

Sampling

Sample interval = time between samples (s)

Sample rate = sample per second (Hz)

44 100 Hz is standard sample rate

Quantisation

Sampled audio is quantised into signed integers

Reading is taken and mapped at each sample interval

24 bits is standard bit depth

Sound trade-offs

Higher bit depth / sample rate: more values and points on the wave, makes digital representation closer to analogue original

More data so more storage - more values/samples

Diminishing returns - humans can no longer tell the difference

Fidelity

How high quality the sound is when played through a device

Product of the device’s quality, not the accuracy of the conversion

Sound file size calculation

File size in bits = sample rate x bit depth x time

Stereo means double the size (2 channels)

CD quality

44 100Hz, 16-bit, 1 411kbps

Benefits of compression

Reduces storage requirements and network transmission time for files

Lossy vs lossless

Lossy

• Audio, videos, images

• Removes unnoticeable data

• Greater size reduction

• Original cannot be reconstructed

• Repeated compression leads to further degradation

• JPEG, mp4, mp3

Lossless

• Mainly text files

• Encodes data

• No reduction in quality when loaded into a program

• Smaller size reduction

• Original can be reconstructed

• ZIP, PNG, PDF

Compression trade-offs

Cost of transmitting uncompressed files may be < decompression cost

Decompression cost may be worth it if short on storage

Lossy loses data and so the original cannot be reconstructed