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4.1 Swithcing Algebra

4.1 Swithcing Algebra - Combinational: itscurrentinputs...

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Analysis and Synthesis:   Analysis start with a logic diagram and proceed  to a formal description of the function performed  by that circuit, such as a truth table or a logic  expression. 4.1   Switching Algebra Return Next 1. Introduction   Logic circuits are classified into two types:  Combinational: whose outputs depend only on  its current inputs.  Sequential: depend not only on the current  inputs but also on the past sequence of inputs,  possibly arbitrarily far back in time.

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4.1   Switching Algebra Next Back Return  Synthesis  do the reverse, starting with a formal  description and proceeding to a logic diagram. 2. Axioms 1+0=0+1=1 A5’ 0 · 1=1 · 0=0 A5 0+0=0 A4’ 1 · 1=1 A4 1+1=1 A3’ 0 · 0=0        A3 if x=1, then x=0 A2’ if x=0, then x=1 A2 x=1 if x 0 A1’ x=0 if x 1 A1
4.1   Switching Algebra Next Back Return 3. Theorems with One Variable x · x=0  T5’ x+x=1 T5 T4’ x =x T4 x · x=x   T3’ x+x=x T3 x · 0=0  T2’ x+1=1 T2 x · 1=x   T1’ x+0=x T1 Identities Null elements Idempotency Complements Involution

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4.1   Switching Algebra Next Back Return 4. Theorems with multi-variable I x · y+x · z=x · (y+z) T8 (x+y)+z=x+(y+z) T7 x+y=y+x T6 (x+y)  · (x+z)=x+y · z T8’ (x  · y)  · z=x · (y · z) T7’ x · y=y · x T6’ Commutativity Associativity Distributivity
4.1

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