From-Transistors-to-Gates

  • Claude Shannon

    • His master's thesis in 1937, A Symbolic Analysis of Relay and Switching Circuits, is considered as "possibly the most important, and also the most famous, master's thesis of the century.”
    • He came up with the idea that electrical switches can be used to do Boolean logic
      SwitchtoBooleanExpression

  • Relay 继电器

  • Vacuum Tube 真空管

  • Transitor 晶体管

Transistor

A transistor is a discrete electronic component that can behave like a switch 可视为开关

  • Tiny, cheap, flexible and reliable
    • onducts when VGS is high (N Type transistor) (close)
    • Blocks when VGS is 0 (open)

CMOS Transistors

Complementary Metal-Oxide Semiconductor 互补金属氧化物半导体

  • Two types: P-type (positive) and N-type (negative)
    • P-type
      • Open (insulating) if gate is “on” = 1 激活时(1)阻断
      • Closed (conducting) if gate is “off” = 0 休眠时(0)导通
    • N-type
      • Open if gate is “off” = 0 激活时(1)导通
      • Closed if gate is “on” = 1 休眠时(0)阻断

Logical Gates

Boolean functions are implemented in digital computer circuits called logic gates.

  • A gate is an electronic device that produces a result based on two or more input values.
  • In reality, gates consist of one to six transistors, but digital designers think of them as a single unit.
  • Integrated circuits contain collections of gates suited to a particular purpose.

Inverter Gate (NOT) 非

  • In = 0v -> P conduct N insulate -> Out is 1 (2.9 v)
  • In = 1v -> P insulate N conduct -> Out is 0 (0 v)

AND/NAND Gate 与

AND consists of NAND and NOT gates.

NOR Gate 异或

OR Gate 或

OR Gate consists of NOR and NOT gates.

Universal Logical Gate

A universal gate is a gate which can implement any Boolean function without need to use any other gate type.

  • The NAND and NOR gates are universal gates.
  • Demorgans'Law

Prove NAND is a universal gate

Prove NOR is a universal gate

Demorgans'Law 记忆技巧

  • 帽子不变,一分一和
Table Of Contents
From-Transistors-to-Gates
Transistor
CMOS Transistors
Logical Gates
Inverter Gate (NOT) 非
AND/NAND Gate 与
NOR Gate 异或
OR Gate 或
Universal Logical Gate
Prove NAND is a universal gate
Prove NOR is a universal gate