PowerPoint

課本PowerPoint

課本詳盡解釋

個人注解

這次Chapter2的上課PowerPoint有3part

而且有很多沒有理解的東西

故篇幅會較大

Part 1

  • Part 1在介紹Binary Logic

Binary Logic and Gates

  • Binary variables take on one of two values.
  • Logical operators operate on binary values and binary variables.
  • Basic logical operators are the logic functions AND, OR and NOT. and, or not是基本的logic operators (不意外)
  • Logic gates implement logic functions. (要不然啦)
  • Boolean Algebra: a useful mathematical system for specifying and transforming logic functions.
  • We study Boolean algebra as a foundation for designing and analyzing digital systems! (最基礎的說)

注意:

在數位邏輯中 $+$ 指的是or,而 $\cdot$ 則是指and

而且此書很喜歡用$\times$當作 $\cdot$ ,但其實$\times$是錯的符號

The three basic logical operations are:

  • AND
  • OR
  • NOT

AND is denoted by a dot (·).

OR is denoted by a plus (+).

NOT is denoted by an overbar ( ¯ ), a single quote mark (‘) after, or (~) before the variable.

Hello World

而圖中所指則是Logic Function其實可以透過簡單的Switches去實現出來

而這一Part比較重要的則是Boolean Algebra的一些公式


Boolean Algebra
1. $x+0=x$ 2. $x\cdot 1=x$
3. $x+1=1$ 4. $x\cdot 0=0$
5. $x+x=x$ 6. $x\cdot x=x$
7. $x+\bar{x}=1$ 8. $x\cdot \bar{x}=0$
9. $\bar{\bar{x}}=x$
10. $x+y=y+x$ 11. $xy=yx$ Commutative
12. $(x+y)+z=x+(y+z)$ 13. $(xy)z=x(yz)$ Associative
14. $x(y+z)=xy+xz$ 15. $x+yz=(x+y)(x+z)$ Distributive
16. $\overline{(x+y)} = \bar{x}\cdot\bar{y}$ 17. $\overline{x\cdot y}=\bar{x}+\bar{y}$ DeMorgan’s

看上去很容易,但真正做題目的時候就知道有多難 …