Principles of Computer Organization (six)

Data representation

Data encoding and representation

• Need to represent objects in a computer
  program, integer, floating point, character (string), the logic value
  represented by encoding
• Representation
  is represented by two states of the digital circuit
  layer abstraction by the computer to identify different content
• Coding principles
  few simple basic symbols
  certain rules
  represent a large number of complex information
  easy to use

Coded representation

• The basic elements of
  0,1 two symbolic
• Character
  26 letters -> 5
  / lower case + other symbols = 7bits (in 8)
  text in other languages in the world = 16bits (unicode)
• Unsigned integer (0, 1, ..., $2^{n}-1$）
• The logic value
  0-false 1-true
• colour
• Location / address / command
• But as the only representative of n $2^{n}$ different objects

Logical Data

• Logical
  true true
  false false
• Data are expressed
  . 1
  0
• Data operations
• And, or, not

x	Y	x and y	x or y	The non-x
0	0	0	0	1
0	1	0	1	1
1	0	0	1	0
1	1	0	1	0

Character data

• Important man-machine interface

• Consisting of symbols
  encoded for each symbol, is converted by the input / output device
  typically in the form of a string stored in a computer memory

• Standard character set encoding
  the ASCII
  the UNICODE
  UTF-. 8

• ascii characters coded
  using 7-bit binary code, one byte
  represents a Western character 128
  ascii code character set
  

• unicode encoded
  using 16 bits represent a character, the character can represent 65536
  the entire space is divided into encoding blocks, each block is a multiple of 16, according to block allocated
  Reserved 6400 yards points for local use
  still can not cover all of the characters

• utf-8 encoded

Number of characters	Byte 1	Byte 2	Byte 3	Byte 4	Byte 5	Byte 6
7	0ddddddd
11	110ddddd	10dddddd
16	1110dddd	10dddddd	10dddddd
21	11110ddd	10dddddd	10dddddd	10dddddd
26	111110dd	10dddddd	10dddddd	10dddddd	10dddddd
31	1111110d	10dddddd	10dddddd	10dddddd	10dddddd	10dddddd

Variable-length character encoding, improve utilization of storage space
character is determined by the length of the first byte of
the character outside the first byte, are "10" begins, self-synchronization
scalability
becomes dominant Internet character set

Represents a numeric data

• Fixed point
  decimal position is fixed
  integer
  fixed-point decimal

• Floating point
  decimal floating position

• Binary representation of the integer
  two states and a binary 0. 1
  n-bit available $2^{n}$ combinations, may represent $2^{n}$ integers

Machine representation	True value
0	0
01	1
10	2
11	3
100	4
101	5
…	…
1{n}	$2^{n}-1$

• evaluation standard
• Unsigned
• It represents the range
• Intuition
• Easy to implement arithmetic operations
• • Signed number
    represents the range of
    visual
    negative balance
    facilitate arithmetic

Binary notation

Binary notation
$\sum_{i=m}^{-k}{D_{i}R^{i}}$
N represents a numerical value
and r represents the radix number
i represents the bit number of symbols arranged
$D_{i}$Is the bit number of one symbol position i
$r^{i}$ is a value represented by a 1 in the bit number i

• Common number system
  decimal, binary, octal, hexadecimal

Hexadecimal and binary notation

Binary
r = 2, 01 basic symbols
octal
r = 8, the basic symbol 01234567
decimal
r = 10, the basic symbol 0123456789
hex
r = 16, the basic symbol 0 1 2 3 4 5 6 7 8 9 ABCDEF
computer binary

Into binary representation of an integer
specific to the n-bit unsigned binary integer, such
$b_{n-1}b_{n-2}...b_{1}$
among them $b_{i}$0 or 1 is
represented by the value N = $\sum_{i=0}^{n-1}{b_{i}2^{i}}$
range represented by 0 ------ $2^{n}-1$ , a total of $2^{n}$ number.

How to represent a signed integer

• We needed to represent a symbol bits
  highest bit
  0 represents an integer, 1 for negative
• Other bits represent data

Anti-code complement the original code

Negative forms
of the original code: the absolute value of the sign bit number ||
anti-code: the symbol bit values ||
complement: the inverted least significant bit + 1

coding	Original code	Inverted	Complement
000	0	0	0
001	1	1	1
010	2	2	2
011	3	3	3
100	-0	-3	-4
101	-1	-2	-3
110	-2	-1	-2
111	-3	-0	-1

Nature complement

Corresponding to the complement of the true value

• Realistic complement value
  N = $-b_{n-1}*2^{n-1}+\sum_{i=0}^{n-2}{b_{i}2^{i}}$
• True value twos complement
  positive numbers complement absolute value of the original code is
  negative complement absolute value of the original code bit negated, then add 1 to the least significant bit
• Complement addition operation of
  the adder sign bit and data bits calculated in the same
  [x + y] Complement = [x] Complement + [y] Complement
  [x] and complement [the -X-] Complement
  [x] in the same complement sign bit, inverted bit by bit, then the lowest bit plus 1, can be obtained [the -X-] complement

Complement subtraction
[XY] Complement = [x] Complement + [- y] Complement

Big-endian and little-endian

0x12345678

Small end large end 78563412 12345678