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Numbers character Coding system - Coggle Diagram
Numbers character Coding system
Denary, Binary and Hexadecimal Number Systems
Binary Number Systems: Computers use it for data representations and manipulations.
Hexadecimal Number System: Programmers use it to communicate with computers.
Denary Number systems : We use it in our daily life for counting and calculation
Number system conversion
Hexadecimal to denary
In the hexadecimal number system, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F are used.
A, B, C, D, E, F represent 10, 11, 12, 13, 14, 15 respectively.
a Denary Number to a Binary Number or a Hexadecimal Number
To convert a denary number to another number system with base b
Divide the denary number by b repetitively until the quotient is smaller than b.
Obtain the answer by writing up from the quotient to the remainders in reverse order.
Binary to denary
Only digits 0 and 1 are used in the binary number system.
a Hexadecimal Number to a Binary Number
To convert a hexadecimal number into a binary number:
Convert each digit of the hexadecimal number into a group of four binary digits.
Obtain the binary number by grouping all the binary digits together.
a Binary Number to a Hexadecimal Number
To convert a binary number into a hexadecimal number:
Group the digits of the binary number by four starting from the righthand side.
Replace each group of the four digits by an equivalent hexadecimal digit.
Number Representation in Computer Systems
Bit, Byte and Word
bit
A single binary digit
The basic unit for storing data in a computer
A single bit can only represent two distinct values.
If more distinct values need to be represented, a series of bits can be used.
An n-bit binary number can represent 2^(n) distinct values.
byte
A data unit used in computers
Consists of 8-bit and is the smallest addressable unit in a microprocessor.
word
Modern computers can handle data stored in two or more bytes at a time.
The natural unit of data used by a computer is called a word.
Modern computers usually have a word length of 16, 32 or 64 bits.
The world length (word size) is measured in bits.
Binary number system
storing number
performing number
the different of each unit is 2^10 times
small to large
÷
large to small
×
Representationof signed Binary Iatnger
sign and pregarftuall
The leftmost bit, known as signal bit, is used to specify the sign of a binary integer.
sign bit
0:a 2 integer
0:a 2 integer
Addition and Subtraction of Different Number Representations
The calculation on both addition and subtraction of unsigned integers in other number systems is the same as that in the denary system.
A ‘borrow’ is generated when the sum of digits equals or exceeds the base value.
A ‘carry’ from the left digit is necessary if a larger digit is subtracted from a smaller one.
Over flow error
Occur when the calculation result is outside the range that the digits can represent.
Occur when the calculation result is the range that the digits can represent.
Overflow error occurs when two numbers of the same sign are added and the result has the opposite sign.
No matter what the sign bits are, the addition of two’s complement numbers are exactly the
same as the addition of two unsigned binary integers.
Character Coding Systems
The character coding system is a way to represent characters in a form that can bemanipulated efficiently in a computer.
ASCII
Two common character coding systems:
America Standard code for information Interchange
Extended Binary-Coded Decimal Interchange code
Each code represents either a printable character or a non-printable character
Each ASCII character consists of 7-bit and it can contain 2^7 different characters.
They include all the alphanumeric characters and graphics symbols.
Other than numeric data, a computer needs to store and process characters.
Chinese Character Coding system
The extended ASCII:
_
characters
There are more than
_
Chinese characters and we use more than 10,000 of
them in our daily lives.
Chinese characters are usually represented in:
The standard ASCII:
__
characters