Hex
# Recall: Two’s Complement
-20 10100
010100 101011
101100
-32 100000 0100000 1011111 110000
-20 + 16 101100c
10000 010000
1011111
| 1 | 0 | 1 | 1 | 0 | 0 |
|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | 1 | 1 |
| 1 0 1 1 0 1 0 1 1 |
1010011
-39 -83
39
101001
83
101011
0101001 0101011
1010110 1010100
| 1 | 0 | 1 | 0 | 1 | 1 | 0 |
|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 1 | 0 |
| Carries: | 1 | 1 |
0001010
-21 + 37
21
010101
37
100101
0010101 0100101
# Hexadecimal
Hex is a base 16 system, each nibble is can be represented with 1 digit.
It is easier to use for humans than basic binary.
The memory location in a computer is stated in hexadecimal form. This makes memory addresses much easier to read.
# Binary to Hexadecimal
Left -> Right Numbers are split into 4 bits (nibbles) Replace each nibble with a hex equivalent
214
128 64 32 16 8 4 2 1 1 1 0 1 0 1 1 0
11010110
1101 0110 D 6
10010100
1001 0100 9 4
128 64 32 16 8 4 2 1 1 0 0 1 0 1 0 0 128 + 16 + 4 = 148
# Applications of Hexadecimal
- Colour representation (#RRGGBB)
- Errors
- Error messages can contain a hex number that contains a memory location to the error
- Very beneficial to programmers
- Errors can be easily rectified by looking at the code in the particular memory location.
- The process in which the contents of the memory is displayed or stored in a specific drive in case of a system crash is called a memory dump.
- Programmers must have knowledge of computer architecture
- MAC addresses
- A Media Access Control address refers to the number that the internet that uniquely identifies a device on the Internet.
- The address is for the NIC (Network Interface Card)
- A MAC address is 48 bits long.
- The first half represents an identification number of the manufacturer, and the second half represents the serial number of the device.
- There are 2 types of MAC address, UAA and LAA. UAA is set by the manufacturer and the LAA can be set by an individual. UAA is most commonly used.
- It is crucial that a UAA is unique.
- Occasionally represented in different formats, but always the same actual data.
- URLs
- Used to represent URLs with ASCII.
- % is used to denote that hex is being used
- Improves security
- Assembly code and machine code
- Hex can refer to memory locations directly
- Hex makes low-level programming easier as it reduces the chance of a mistake.
- HTML
# Recall
SIGN 64 32 16 8 4 2 1 00011001 16+8+1 = 25
+32
00100000
10000110
SIGN+2+4 = -6
01111111 64+32+16+8+4+2+1 127
-16
1001000
12^10 = 0xC
128^10 = 0x80
250^10 = FA
20^16 = 32