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)
⚠Similar question could be: explain why data needs to be converted to binary.
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
⚠Think about the hexadecimal error code 404, the binary equivalent is:010000000100.Which is easier to memorise?
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
Example 1: 2 Left logical shifts on00010011
- Result:01001100
- The number has been multiplied by 2 to the power of 2
Example 2: 2 Left logical shifts on11010011
- Result:01001100
- Most significant bits are lost. The answer is incorrect
⚠Before you answer these questions look at what is happening to your binary register. If a left most bit is lost use Example 2 answer, otherwise Example 1.
- Left shifts = multiplication by 2^number of shifts
- Right shifts = division by 2^number of shifts