From Transistors To Gates

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)

  • 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

AND consists of NAND and NOT gates.

NOR Gate 异或

OR Gate

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
    • $\overline{X*Y}=\overline{X}+\overline{Y}$
    • $\overline{X+Y}=\overline{X}*\overline{Y}$

Prove NAND is a universal gate $\overline{XY}$

  • $NOT: \overline{X}=\overline{XX}$
  • $OR: X+Y=\overline{\overline{X}}+\overline{\overline{Y}}=\overline{\overline{X}*\overline{Y}}$
  • $AND: XY=\overline{\overline{XY}}$

Prove NOR is a universal gate $\overline{X+Y}$

  • $NOT: \overline{X}=\overline{X+X}$
  • $OR: X+Y=\overline{\overline{X+Y}}$
  • $AND: XY=\overline{\overline{X}}*\overline{\overline{Y}}=\overline{\overline{X}+\overline{Y}}$

Demorgans’Law 记忆技巧

  • $* -> +$ 帽子不变,一分一和
    • $\overline{X*Y}=\overline{X}+\overline{Y}$
    • $\overline{X+Y}=\overline{X}*\overline{Y}$

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