Trace Through Calculations

Work through file size calculations step by step

How to Use This Activity

Complete each calculation step by step. Enter your answer, then check if you're correct before moving on. This helps you understand the process, not just get final answers.

Exercise 1: Text File Size (ASCII)

Calculate the file size of a text file containing "Computer Science is fun!" (24 characters) using ASCII encoding.

Step 1: How many characters are in the text?

Step 2: ASCII uses how many bits per character?

Step 3: File size in bits = 24 × 8 = ?

Step 4: File size in bytes = 192 ÷ 8 = ?

Exercise 2: Unicode File Size Comparison

A document contains 1,000 characters. Calculate the file size in both ASCII (8-bit) and Unicode (16-bit).

Part A: ASCII

Step 1: ASCII file size in bits = 1,000 × 8 = ?

Step 2: ASCII file size in bytes = 8,000 ÷ 8 = ?

Part B: Unicode

Step 3: Unicode file size in bits = 1,000 × 16 = ?

Step 4: Unicode file size in bytes = 16,000 ÷ 8 = ?

Part C: Comparison

Step 5: How many times larger is Unicode than ASCII? (2000 ÷ 1000)

Exercise 3: ASCII Character Codes

Using the pattern that 'A' = 65, 'a' = 97, and '0' = 48, calculate the codes for other characters.

Step 1: 'E' is the 5th letter. Code for 'E' = 65 + 4 = ?

Step 2: 'e' is lowercase. Code for 'e' = 69 + 32 = ?

Step 3: '5' is 5 positions after '0'. Code for '5' = 48 + 5 = ?

Step 4: 'Z' is the 26th letter. Code for 'Z' = 65 + 25 = ?

Exercise 4: Image File Size

Calculate the file size of a 640 × 480 pixel image with 24-bit colour depth.

Step 1: Total pixels = 640 × 480 = ?

Step 2: File size in bits = 307,200 × 24 = ?

Step 3: File size in bytes = 7,372,800 ÷ 8 = ?

Step 4: File size in KB = 921,600 ÷ 1,000 = ? (round to 1 decimal)

Exercise 5: Colour Depth Comparison

An image has 500,000 pixels. Compare file sizes at different colour depths.

Step 1: At 1-bit colour, how many colours are possible? (2^1)

Step 2: File size at 1-bit = 500,000 × 1 = ? bits

Step 3: At 8-bit colour, how many colours are possible? (2^8)

Step 4: File size at 8-bit = 500,000 × 8 = ? bits

Step 5: How many times larger is 8-bit than 1-bit?

Exercise 6: Sound File Size (Mono)

Calculate the file size of a 20-second mono recording at 22,050 Hz sample rate with 8-bit depth.

Step 1: Total samples = 22,050 × 20 = ?

Step 2: File size in bits = 441,000 × 8 = ?

Step 3: File size in bytes = 3,528,000 ÷ 8 = ?

Step 4: File size in KB = 441,000 ÷ 1,000 = ?

Exercise 7: CD Quality Stereo Sound

Calculate the file size of a 1-minute stereo track at CD quality (44,100 Hz, 16-bit).

Step 1: Duration in seconds = 1 × 60 = ?

Step 2: Samples per channel = 44,100 × 60 = ?

Step 3: Bits per channel = 2,646,000 × 16 = ?

Step 4: Total bits (stereo = 2 channels) = 42,336,000 × 2 = ?

Step 5: Bytes = 84,672,000 ÷ 8 = ?

Step 6: MB = 10,584,000 ÷ 1,000,000 = ? (2 decimal places)

Exercise 8: Sample Rate Impact

Compare file sizes for a 30-second mono recording at different sample rates (all 16-bit).

Telephone Quality (8,000 Hz)

Step 1: Bits = 8,000 × 16 × 30 = ?

Step 2: Bytes = 3,840,000 ÷ 8 = ?

CD Quality (44,100 Hz)

Step 3: Bits = 44,100 × 16 × 30 = ?

Step 4: Bytes = 21,168,000 ÷ 8 = ?

Comparison

Step 5: CD quality is how many times larger than telephone? (round to 1 decimal)

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