Simplification of Boolean functions

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Draft notes or 22C: 0402Simplification of Boolean functionsUsing the theorems of Boolean Algebra, the algebraicforms of functions can often be simplified, which leads tosimpler (and cheaper) 1F = + + (B + B) + How many gates do you save= + from this Simplification ?=A + FBFCCDraft notes or 22C: 0403Example 2F= + + + + + + + + ( + ) + ( + ) + ( + )=(A + A). + (B + B). + (C + C). + + 3Show that A + = AA + AB= + (1 + B)=A. 1=ADraft notes or 22C: 0404Simplification using Karnaugh MapsAB01101K-map of 2-variable OR function011BCA000111100 11111K-map of majority functionFollow the class lectures to understand how tosimplify Boolean functions using K-maps. Severalexamples will be worked out in the notes or 22C: 0405Other types of gatesAA A+BBNAND gateNOR gateBe familiar with the truth tables of these + B = + OR (XOR) gateDraft notes or 22C: 0406NAND and NOR are universal gatesAny function can be implemented using only NANDor only NOR gates.

Simplification of Boolean functions Using the theorems of Boolean Algebra, the algebraic forms of functions can often be simplified, which leads to simpler (and cheaper) implementations. Example 1 F = A.B + A.B + B.C = A. (B + B) + B.C How many gates do you save = A.1 + B.C from this simplification? = A + B.C A A B F B F C C

  Functions, Gate, Boolean, Boolean functions