1.1 Number Systems

Denary, Binary & Hexadecimal

• Binary system: Base 2. Only has 2 values. Represented using 0 and 1.
• Denary system: Base 10. Has 10 values. Represented with numbers from 0–9.
• Hexadecimal: Base 16. Has 16 values. Represented with symbols 0–9 and letters A–F.

Explain why a computer can only process binary data

• Computer consist of transistors/logic circuits
• …that can only store process data in two states (on/off)

Uses of Hexadecimal

• Error codes. Eg #404
• HTML colour codes. Eg FFFFFF
• URL
• Memory Dump
• IP addresses
• Assembly language
• ASCII/Unicode

Why do Developers prefer to use Hexadecimal?

• Easier/quicker to understand/read/write
• Easier/quicker to debug
• Less likely to make a mistake
• Shorter representation // Takes up less screen space

Describe a similarity & difference between Binary and Hexadecimal

• They are both number systems

• Binary is base 2 whereas hexadecimal is base 16
• Binary only uses numbers whereas hexadecimal also uses letters // Binary only uses 0 and 1 whereas hexadecimal uses 0 to 9 and A to F

MAC Address

• Made up of 48 bits
• Shown as 6 groups of two hexadecimal digits
• First half represents Manufacturer
• Second half represents Serial number
• Uniquely identifies a device on the network
• eg. 11:11:11:11:11:11
• MEDIA ACCESS CONTROL (only use if not referred to by the question!)

Overflow Errors

• A computer has a predefined limit that it can represent (eg. 8 bits)
• …Overflow occurs when a value outside this limit should be returned

• Can occur when two binary numbers are added together
• …the result cannot be represented in the current register.
• eg. 255+10 in binary cannot be represented in the current size of the register.
• Solution: use a 16 bit/2 byte register

What Effect does a Logical Shift have on a binary number

• Left shifts = multiplication by 2^{number of shifts}
• Right shifts = division by 2^{number of shifts}