A1.2 Data representation and computer logic: notes and practice

What you need to know

Our summary of the topic in our own words, not the IB guide.

• Explain why computers represent all data in binary
• Convert between denary, binary and hexadecimal
• Calculate the number of distinct values a given number of bits can represent
• Explain the relationship between bits, bytes and the common size prefixes
• Explain how integers are stored, including a representation for negative numbers
• Explain how characters and strings are stored using a character encoding such as ASCII or UTF-8
• Explain how a bitmap image is stored, and how resolution and colour depth affect file size
• Compare raster and vector image representation
• Explain how sound is digitised, and how sample rate and bit depth affect quality and file size
• Explain how video is stored and why frame rate, resolution and compression drive file size
• State the purpose of a logic gate and name the common gates AND, OR, NOT, NAND, NOR and XOR
• Write the Boolean expression for a described condition
• Construct a truth table for a single gate
• Construct a truth table for a multi-input Boolean expression, applying the correct order of operations
• Use a Karnaugh map to simplify a Boolean expression
• Draw a logic circuit diagram from a Boolean expression
• Derive the Boolean expression and truth table from a given logic circuit diagram

Practice questions

Original questions written for the 2027 course, marked as you go. Easiest first.

• Binary and hexadecimal: a brightness byteWritten · Core
• Bitmap file size for a wildlife cameraWritten · Stretch
• Logic gates for a greenhouse warning lightWritten · Stretch
• Two's complement for a freezer logWritten · Stretch

Exam tips for A1.2

• Show your working in conversions and file size calculations. A method mark can survive one slip in arithmetic.
• For truth tables, list the inputs in binary counting order (000, 001, 010 and so on) so you never miss a row.
• Remember NOT applies before AND, and AND before OR, unless brackets say otherwise.