Number systems

Convert denary to binary

Divide by 2 for x remainder y. Write y in place value and divide x by 2 again. Repeat

Convert denary to hex

Divide by 16 for x remainder y. Write y in hex form in place value and divide x by 16 again. Repeat

What is a bit?

A single 0 or 1

What is a nibble?

4 bits (1010)

What is a byte?

8 bits (10101010) / 2 nibbles

Hex to binary

Map values one digit at a time

Binary to hex

Map values one nibble at a time

Why use hexadecimal?

less display space needed; faster to enter data; easy to convert back to binary; easier to identify values and spot errors

Example usages of hex

Colour coding when formatting web pages in HTML or CSS; low-level code; addresses; error messaging

What indicates that a colour is being coded in hex?

#

How do hex colour codes work?

2 hex digits for each of RGB

White in hex

FFFFFF

Red in hex

FF0000

Black in hex

000000

What does the value of the hex numbers represent?

Intensity of colour

When might you see hex options when setting colour values?

Graphics packages e.g. Adobe creative suite apps

How are hex colour codes used in laser cutters?

Identify how to set laser strength and depth of cut

Why is hex used in assembly code?

Quicker, easier and less error prone for programmers to type assembly code values in hex than long binary strings

How do programmers make it more efficient to troubleshoot low level code?

Using hexadecimal instead of typing out long binary strings

How is hex used in addresses?

Both IP and MAC addresses

What do MAC addresses do?

Media access control - uniquely identify devices on a network

Where do devices get their MAC addresses from?

Assigned by device manufacturer

What are MAC addresses made of?

6 pairs of hex digits NN-NN-NN-DD-DD-DD

What is the NN-NN-NN in MAC addresses

ID of manufacturer

What is the DD-DD-DD in MAC addresses

serial number of device

Which comes first in a MAC address - NN-NN-NN or DD-DD-DD

NN-NN-NN

What do IP addresses do?

Internet Protocol - identify where a device is on a network

What number system are IP version 4 addresses?

decimal

What are IP version 6 addresses?

hex

Which uses hex - IP version 4 or version 6

Version 6

What does IPv6 do?

Provides enough unique addresses for every networked device on the planet

How are IPv6 addresses organised?

128 bits; digits organised in 8 groups; 4 hex digits per group

How many bits in an IPv6 address?

128

Where is hex used in error messaging?

Display of error codes in embedded systems e.g. lifts

Why are hex codes used in error messaging?

Embedded systems have tiny screens if any; hex takes up less space than binary