A216
Basics Facts and Equations.

Last Updated: November 8, 2023

Below are facts and equations we will expect you to know and learn for A216. We will add to this list as we progress in the course. On occasion, a fact or equation may appear here before we discuss it in class or lab.

We will expect you to know these facts and equations for a quiz or assignment only after we have discussed or mentioned them in lecture or lab.

While some of this may seem simple to some of you, we want to make sure every one has equal access to these basic resources.

Also note that some of these facts you should not have to memorize. For example: If you know what a kilobyte (kB) is, how many kB in a GB (Gigabyte) and how many bits in a byte, then you can calculate how may bits in a GB. I have given you this fact below just to be complete.

Basic Facts for A216.

1 bit can have either value 1 or value 0

1 byte = 8 bits

1 kilobit (kb) = 1000 bits

1 kilobyte (kB) = 1024 bytes = 8192 bits

1 Megabit (Mb) = 1000 kb = 1,000,000 bits

1 Megabyte (MB) = 1024 kB = 1,048,576 bytes = 8,388,608 bits

1 Gigabit (Gb) = 1000 Mb = 1,000,000,000 bits

1 Gigabyte (GB) = 1024 MB = 1,073,741,824 bytes = 8,589,934,592 bits

In other contexts "kilo" (k) usually means 1,000

In other contexts "mega" (M) usually means 1,000,000

In other contexts, "giga" (G) usually means 1,000,000,000

A "Hertz" (Hz) is a "cycle per second." So a kiloHertz (kHz) is 1000 cycles/sec.

Example: "22kHz" [22 kiloHertz] means 22,000 cycles/second

Example: "3MHz" [3 MegaHertz] means 3,000,000 cycles/second

Example: "4GHz" [4 GigaHertz] means 4,000,000,000 cycles/second

Time.

1 minute = 60 seconds

1 hour = 60 minutes = 3600 seconds

Powers of 2.

8 bits means 2⁸ possible combinations = 256

16 bits means 2¹⁶ possible combinations = 65,536

24 bits means 2²⁴ possible combinations = ~ 16.7 million [16,777,216]

32 bits means 2³² possible combinations = ~ 4.29 billion [4,294,967,296]

Audio Memory, Bitrates, Sampling rates, and Storage.

3 relevant factors: Sampling rate, bits/sample, Mono/Stereo/Multichannel.

Sampling rate is usually in kHz (1000s of cycles/second).

Bits/sample is usually either: 8-bits/sample, 16-bits/sample, 24-bits/sample. [Note that this is identical to 1-byte/sample, 2-bytes/sample, and 3-bytes/sample.]

Mono means one channel, Stereo means two channels (twice as much data), and multi-channel means 3 or more channels (even more data).

EXAMPLE: Sampling rate: 32kHz, 16-bits/sample, Mono.

How much date per second in bits?

32,000 x 16 = 512000 bits/sec. (Stereo: 1024000 bits/sec)

How many kb/sec?

512000/1000 = 512 kb/sec. (Stereo: 1024 kb/sec or 1.024 Mb/sec)

How many kB/sec?

512000/8 = 64000 bytes/sec 64000 bytes/sec / 1024bytes/kB = 62.5 kB/sec. (Stereo: 125 kB/sec)

[Make sure you understand the differences between the above questions and their answers.]

Displays and Aspect Ratios.

Standard Television is 4:3 [Width: Height].

"Widescreen" or HDTV is 16:9.

4:3 can also be written as 1.33:1

16:9 can also be written as 1.78:1

Aspect ratio for film called "flat" or "spherical" is 1.85:1.

Aspect ratio for film called "anamorphic" or "scope" is 2.35:1.

Basic Equations for A216.

Video Display Memory

How many MBs of video memory to support a certain resolution and color depth?

EXAMPLE: Resolution = 1024 x 768; Color Depth = 16-bits/pixel.

1024 x 768 = 786432 pixels.

16-bits/per pixel means 2-bytes/pixel.

786432 pixels x 2-bytes/pixel = 1,572,864 bytes of video memory required.

1,572,864 bytes / 1024 bytes/kiloByte (kB) = 1536 kB of video memory.

1536 kB / 1024 kB/Megabyte (MB) = 1.5 MB of video memory.

Scanning, dpi and such.

If you need to figure out how big your scanned image will be in bits or bytes.

Original physical dimensions of scanned object (in inches) x scanning resolution (in dpi). This will yield dimension in pixels. Together with bits/pixel, you should be able to calculate the file size.

EXAMPLE: 2 x 3 inches @ 300dpi = 600 x 900 pixels, or 540000 pixels. 16-bits/pixel x 540000 pixels = 8640000 bits, or 1080000 bytes, or 1054.6875 kB, or 1.0299MB.

Digital Video Memory, Bitrates, Color Depth/Resolution, and Storage.

Crucial things you need to know will include:

• What is the screen or image size in pixels x pixels?
• What is the color depth in bits/pixel?
• How many frames/second are being presented?
• Is there audio? If so, what is the sampling rate and bits/sample?

EXAMPLE: With a screen size of 320x240, a color-depth of 24 bits/pixel, a frame rate of 30 frames/second and 22kHz, 16-bit mono sound, what is the bitrate?

Screen size of 320x240 = 76800 pixels/frame.

24-bits/pixel x 76800 pixels = 1843200 bits/frame

1843200 bits/frame x 30 frames/sec = 55296000 bits/second for video only

AUDIO: 22000 samples/sec x 16-bits/sample = 352000 bits/second.

TOTAL: 55296000 bits/second + 352000 bits/second = 55648000 bits/second.

55296000 bits/second / 1000 bits/kilobit = 55648 kb/sec

55648 kb/sec / 1000kb/Mb = 55.648 Mb/sec

Now, suppose you want to find out how much space it takes to store a file of 15 seconds duration using these parameters. REMEMBER, storage is always in bytes, kilobytes, or Megabytes. You must do the conversion.

55648000 bits/second / 8-bits/byte = 6956000 bytes/sec.

6956000 bytes/sec x 15 seconds = 104340000 bytes

104340000 bytes / 1024 bytes/kilobyte = 101894.53125 kB.

101894.53125 kB / 1024 kB/MB = 99.50637817383 MB.

In other words, it would take about 100MB to store this 15 second AV file using these parameters.