Chapter 1 Digital Systems and Information

Breif Intro¶

做存储的时候，访问需要字对齐，按照字去取
Cache 局部性原理

Signal¶

The most commonly used two-valued information is an electrical signal - voltage or current typically two discrete values represented by the voltage range of values.

Digital Systems¶

Takes a set of discrete information inputs and discrete internal information (system state) and generates a set of discrete information outputs.

Types of Digital Systems¶

Combinational Logic System:No state present , one input just decide one output(one to one , no state)
Sequential System

State present

State updated at discrete times -- Synchronous Sequential System [Periodic]

State updated att any time -- Asychronous Sequential System

State function : \(f_{state}=Function(State,Input)\)

Output function : \(f_{output}=Function(State)\) or \(f_{output}=Function(State,Input)\)

Organization of Computer¶

Embedded Systems¶

Number Systems & Codes¶

Covert¶

Decimal To Binary¶

整数——权展开式除2，余数构成最低位——除2取余
小数——权展开式乘2，整数构成最高位——乘2取整

Binary Numbers and Binary Coding¶

Non-numeric Binary Codes¶

Given n binary digits (called bits), a binary code is a mapping from a set of represented elements to a subset of the \(2^n\) binary numbers.

Number of Elements Represented¶

You can represent 4 elements in radix r = 2 with n = 2 digits: (00, 01, 10, 11).
You can represent 4 elements in radix \(r=2\) with \(n=4\) digits (0001,0010,0100,1000) \(One\ Hot\ Code\)
Other Examples

For \(8\ 4\ -2\ -1\) \(\&\) \(Excess\ 3\) code -- "Symmetric"(complement) Same Probability for \(0\) and \(1\)
\(Excess\ 3\) code -- (real binary value plus 3)