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1.4.3 boolean algrabra (D type flip flops (uses (regster memry, static ram…
1.4.3 boolean algrabra
defining problems
Not
negation
reverses input
¬
AND
conjuction
A and B is one output is 1 else 0
^
OR
disjunction
a or b is one
∨
XOR
exclusive disjunctionm
diffrent -1
⊕
NAND and NOR
and or then not
efficiency with boolean expressions
order of preferance
Not, AND then OR
brackets still apply
simple rules
¬(¬A)=A
A^¬A=0
Av¬A=1
karnaugh map
input data in too map
draw boxes in orders of 2
separate by the ors
order matters each digit must change one at a time
groups are large as possible
over lapping allowed
wrap around okay
smallest number of groups
rectangles and squres
all ones must be in a group
logic gates and true tables
picture of symbols
truth table
have each input
and the result at each intersection
shows output
boolean algebra rules
De Morgans law
¬(AVB)=(¬A)^(¬B)
¬(A^B)=(¬A)v(¬B)
Disbution
factoriesing
A^(BVC)=(A^B)v(A^C)
Av(B^C)=(AvB)^(AvC)
Association
removal of bracxkets
Av(BvC)=AvBvC
A^(B^C)=A^B^C
comutatio
order does not matter
A^B=B^A
AvB=BvA
double negation
reverse twice
¬(¬A)=A
absortion
terms can be aborbs easyily
Xv(X^Y)=X
X^(XVY)=X
the opertaters on the inside and outside must differ
the terms outside must also be inside
half and full adders
half adder
adds two items together and carryes when it needs two
inputs a and b
outputs digit and carry
diagram
and gate and Xor gate
full adder
combines half adder
inputs A,B ,Carry in
outputs digit and carry out
digram
adders can be connected do do binary addition
D type flip flops
a basic circuit that can store a bit and flip itbetween 0 and 1
it has two inputs a control and a clock
clock constantly changes state at pules
synises changes of state
needed thought computers
positive edge trigged flip flop circuit
out put can only change when clock pulse is postive
the output value does not change
stored as a memory cell
diagram
uses
regster memry
static ram
mulple flip flops means storing mulple data