# Binary numbers exercise

The following exercise will give you a good introduction to working with binary numbers and two’s complement. The skills required for the extension questions are on your syllabus so please make an attempt at them.

Points to note:

• “Denary” means decimal, base 10 (normal counting).

Extension questions:

• Find an expression for the number of values that can be represented using n bits.
• In n-bit two’s complement, find an expression for the maximum and minimum values that can be expressed.
• Without using the binary counter, express -105 in 8-bit two’s complement.
• In the context of this exercise, explain the following statements:
• “4-bit colour representation allows for 16 colours.”
• “A 32-bit address bus can address 4GB of RAM.”
• Discuss the differences between ASCII and Unicode.
• With specific reference to your knowledge of data representation in computer systems, and using temperature sensing as an example, discuss the differences between analogue and digital data, together with the need and method of interconversion between them.
• Investigate how analogue to digital conversion (and vice versa) impacts digital music production. Your answer should address the link between sampling rate and file size. Experiment with some music recording using a variety of sampling rates. Can you tell the difference?