Cheat Sheet

Computer Science · Information representation and multimedia

Key Facts

Explain binary magnitudes, binary prefixes, and decimal prefixes.

Convert between binary, denary, and hexadecimal number systems.

Perform binary addition and subtraction using two's complement.

Describe the use of hexadecimal and binary coded decimal (BCD) number systems.

Explain the representation of character sets like ASCII and Unicode.

Describe how data for bit-mapped images and vector graphics are encoded.

Estimate the file size for a bit-map image based on resolution and colour depth.

Explain the representation of sound in a computer and the effects of sampling rate and resolution.

Discuss the need for and methods of file compression (lossy and lossless formats).

Formulas

Number of colours from bit depth

2^{n}

n

— bit depth (bits)

Used for calculating the number of possible colours in an image given its colour depth, or the number of amplitude values for sound given its sampling resolution.

Bit-map image file size (bits)

File size (bits) = Image width (pixels) \times Image height (pixels) \times Bit depth (bits per pixel)

B i t d e pt h

— number of bits used per pixel (colour depth)

I ma g e w i d t h

— number of pixels horizontally

I ma g e h e i g h t

— number of pixels vertically

This formula calculates the raw uncompressed file size in bits. To get bytes, divide by 8. To get MB or MiB, further division is needed.

Pixel density (ppi)

Pixel density (ppi) = \frac{Horizontal pixels ^{2} + Vertical pixels ^{2}}{Screen size (inches)}

S cr ee n s i z e

— diagonal screen size (inches)

V er t i c a l p i x e l s

— number of pixels vertically on screen

H or i z o n t a l p i x e l s

— number of pixels horizontally on screen

This formula calculates the pixel density in pixels per inch (ppi) for a given screen resolution and diagonal screen size.

⚠ Common Misconceptions

Confusing one's complement with two's complement, especially the 'add 1' step for two's complement.

Misunderstanding that BCD encodes each denary digit separately, rather than converting the entire denary number to binary.

Believing that ASCII can represent all global characters, overlooking the need for Unicode.

Confusing image resolution (total pixels in an image) with screen resolution (pixels on a display device).

Assuming bit-map images can be scaled indefinitely without quality loss, ignoring pixelation.

Mixing up sampling rate (how often samples are taken) and sampling resolution (precision of each sample's amplitude) for sound files.