Unit 8 - Boolean Algebra Flashcards
shape of AND gate and AND symbol
shape = D
symbol = ^
shape of NOT gate and NOT symbol
shape = triangle
symbol = ¬
shape of OR gate and OR symbol
shape = curved triangle thing
symbol = v
shape of XOR gate and XOR symbol
shape = OR gate with extra line
symbol = v̲
what is de Morgan’s first law
¬(A v B) = ¬A ^ ¬ B
what is de Morgan’s second law
¬(A ^ B) = ¬A v ¬B
what are the 8 general rules of boolean algebra
- X ^ 0 = 0
- X ^ 1 = X
- X ^ X = X
- X ^ ¬X = 0
- X v 0 = X
- X v 1 = 1
- X v X = X
- X v ¬X = 1
X ^ 0 = ?
0
X ^ 1 = ?
X
X ^ X = ?
X
X ^ ¬X = ?
0
X v 0 = ?
X
X v 1 = ?
1
X v X = ?
X
X v ¬X = ?
1
what are the commutative rules
- X ^ Y = Y ^ X
- X v Y = Y v X
simplify, reorganise or expand X ^ Y = ? and name the rule used
Y ^ X
commutative
simplify, reorganise or expand X v Y = ? and name the rule used
Y v X
commutative
simplify, reorganise or expand ¬(A v B) = ? and name the rule used
¬A ^ ¬ B
de Morgan’s first law
simplify, reorganise or expand ¬(A ^ B) = ?and name the rule used
¬A v ¬ B
de Morgan’s second law
what are the associative rules
- X ^ ( Y ^ Z) = (X ^ Y) ^ Z
- X v (Y v Z) = (X v Y) v Z
simplify, reorganise or expand X ^ ( Y ^ Z) = ? and name the rule used
(X ^ Y) ^ Z
associative
simplify, reorganise or expand X v ( Y v Z) = ? and name the rule used
(X v Y) v Z
associative
what are the distributive rules
- X ^ (Y v Z) = (X ^ Y) v (X ^Z)
- (X v Y) ^ (W v Z) = (X ^ W) v ( X ^ Z) v (Y ^ W) v (Y ^ Z)
simplify, reorganise or expand X ^ (Y v Z) = ? and name the rule used
(X ^ Y) v (X ^Z)
distributive
simplify, reorganise or expand (X v Y) ^ (W v Z) = ? and name the rule used
(X ^ W) v ( X ^ Z) v (Y ^ W) v (Y ^ Z)
distributive
what are the absorption rules
- X v (X ^ Y) = X
- X ^ (X v Y) = X
simplify, reorganise or expand X v (X ^ Y) = ? and name the rule used
X
absorption
simplify, reorganise or expand X ^ (X v Y) = ? and name the rule used
X
absorption
what is the double negation rule
- X = ¬¬X
simplify, reorganise or expand ¬¬X = ? and name the rule used
X
double negation
what is a karnaugh map
an alternative way of simplifying boolean expressions which is often easier than using boolean algerbra for those using up to three of four variables. it is similar to a truth table and allows us to easily detect grouping with common factors
K-MAPS: sizes of groupings that are allowed
1, 2, 4 or 8 and can be overlapping
K - MAPS: determining groupings
each grouping should be as large as possible
what is a half-adder
a half adder can take an input of two-bits and give a two-bit output as a correct result of an addition of the two bits
adders: what does S represent
sum
adders: what does C represent
carry bit
what is a full adder
a full adder combines two half adders to add three bits together including the two inputs A and B, and the carry bit
logic gate circuit for half adder
logic gate of full adder
what is a D-type flip-flop
a flip flop is an element sequential logic circuit that can store one bit and flip between two states, 0 and 1. a D-type flip flop has one input called D, and two output Q and NOT Q (a clock signal).
what does an edge-triggered flip-flop mean
it stores the value of one bit when a signal is given
- takes in three inputs the clock, D and Q and then on the rising edge of the clock Q will change to D
uses of D-type flip-flops
- D-type flip-flops are used for creating registers and counters
- they are used for intermediate storage needed during arithmetic operations
- static RAM is also created using D-type flip-flops
what does a D-type flip-flop look like
