Data Logic design basics

boolean algerbra:

Some important laws jegula kaje lage dld te.

1.and rules: ->A.A=A ->A.1=A ->A.0=0 ->A.A'=0

2.->A+A=A ->A+A'=1 ->A+1=1 ->A+0=A

3.A+A'B=A+B or A'+AB=A'+B (very important rule)

4.De morgans law: (A.B)'=A'+B' (A+B)'=A'.B'

5.distributive law: ->A.(B+C)=A.B+A.C ->A+(B.C)=(A+B).(A+C)

6.commutative law: ->a(bc)=(ab)c

ai law gula use kore amra circuit design korte pari.law gula use kora hoi mainly logic gate komanor jonno.

kisu imp term: ->maxterm(product of all variables jmn ABC,ABC',A'B'C' etc) ->minterm(sum of all literal or variable jmn A'+B+C, A+B+C' etc) ->canonical form(truth table theke actually jei form ta pawa jai) ->minimal form(canonical a formula use kore choto kore ja pawa jai)

SOP or sum of Products: sum of those cases for which the output function is high(1).Every case is in minterm. F=ABC+A'B'C+......

POS or product of sum: sum of those cases for which the output function is low(0).Every case is in maxterm. F=(A+B'+C).(A+B+C')........

k-Map: Used to solve the boolean algebra without doing it explicitly.In K-map every room is hold 1 bit different then its neighbours.So the soul of K-map is A+A'=1.Group the 1 values in a manner of 16,8,4,2.Rounding is allowed.No diagonal group is allowed cause diagonally the bit change is more than 1.

redundancy rule: ->if all variables are twice and one of them is inverted only then neglect the inverted one. examp: AC+BC'+AB to AC+AB (A,B,C is 2 times and only C is inverted).

redundancy rule is used in Kmap cause some cases we have to group the same thing twice.

MUX:(Multiplexer) Many input but only one output.

there are selectors to select which input should be choosen.

There are several types of MUX.In 2*1 mux there are 2 input channel and one selector In 4*1 there are 4 input channel and 2 selector and so on.So the selector number is log2n.