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Logic Gates Claude Shannon Circuits Boolean algebra Overview of ...

Logic Gates Claude Shannon Circuits Boolean algebra Overview of ...

Logic Gates Claude Shannon Circuits Boolean algebra Overview of

9/10/13 Claude Shannon Logic Gates • Father of information theory CS 231 Dianna Xu • His master thesis was the foundation of digital circuit design theory. 1 2 • Single switch • Switches in series • Switches in parallel Circuits Boolean algebraBoolean – a variable that is either true or false • Boolean algebra – logical calculus of truth values – Very similar to Boolean logic – Variables can only be 1 or 0 • Instead of true / false 3 4 Overview of Boolean algebra • Not _ is a horizontal bar above the number – 0 _ = 1 – 1 = 0 • Or is a plus – 0+0 = 0 – 0+1 = 1 – 1+0 = 1 – 1+1 = 1 • And is multiplication – 0*0 = 0 – 0*1 = 0 – 1*0 = 0 – 1*1 = 1 5 Overview of Boolean algebra _ _ _ • Example: translate (x+y+z)(xyz) to a Boolean logic expression – (x∨y∨z)∧(~x∧~y∧~z) • We can define a Boolean function: _ _ – F(x,y) = (x+y)(xy) = (x∨y)∧(~x∧~y) • And then write a “truth table” for it: x y F(x,y) 1 1 0 1 0 0 0 1 0 0 0 0 6 1

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