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

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