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Chapter 3 coding system Safa and Joyce (3.3 Number representation in…
Chapter 3 coding system
Safa and Joyce
3.1 Denary, Binary, Hexadecimal Number systems
We use denary (base 10) in daily life
Computer uses Boolean logic, binary (base 2)
0s and 1s
Hexadecimal (base 16) used for communication between computers and programmers
3.2 Number System Conversion
We can find corresponding values in the denary number system
convert Denary to Binary:
e.g. 37 = 100101
convert Binary to Hexadecimal
e.g 10011111 = 9F
Convert Hexadecimal to Binary
e.g. A7 = 1010 0111
Convert Denary to Hexadecimal
e.g. 420 = 1A4
3.3 Number representation in Computer Systems
Bit: 1 binary digit, basic unit e.g.8 bit represents 256 distinct values, n-bit represents n^2
Byte: 8 bits, (smallest addressable unit in microprocessor)
Word length = natural unit of processing data
unsigned and signed integer
b=bit, B=byte
1B=8b
1KB=1024b
1MB=1024KB
1GB=1024MB
1TB=1024GB
1PB=1024TB
Two's complement
(study notes)
e.g. 0111=7
1100=-4
3.5 Character Coding System
Character Coding System is a way to represent characters in a form. e.g. Chinese Characters
ASCII is a common character coding system which represents printable or non-printable characters.
Big5 Code is mainly used to represent traditional Chinese Characters
Unicode can represent any language in the world.
e.g. Korean, European Languages
3.4 Addition and Subtraction of Different Number Representations
Calculating it is the same as calculating denary numbers
Overflow Error occurs when the result is outside the range that the digits can represent.