1.4.3 Boolean Algebra Flashcards
How can problems be defined?
Using boolean logic in boolean equations
What results can come from a boolean equation?
True
False
What is the name given to the conjunction operation?
AND
What is the symbol given to the conjunction operation?
ʌ
What is the shape given to the conjunction operation?
D
What is the name given to the disjunction operation?
OR
What is the symbol given to the disjunction operation?
V
What is the name given to the negation operation?
NOT
What is the symbol given to the negation operation?
¬
What is the shape given to the negation operation?
▷
What name is given to the exclusive disjunction operation?
XOR
What symbol is given to the exclusive disjunction operation?
V̲
What is a truth table?
A table showing every possible combination of inputs to a logic gate and corresponding output
How are boolean equations made?
By combining boolean operators
What is a Karnaugh map?
A method of simpiflying boolean expressions
Describe how boolean expressions can be simplified using Karnaugh map.
Write truth table as a Karnaugh map
Highlight groups of 1s in map
Remove variables which change within rectangles
Keep variables which do not change
How can expressions be simplified using De Morgan’s Law?
¬(A ʌ B) = ¬A v ¬B
¬(A v B) = ¬A ʌ ¬B
How can expressions be simplified using Distribution Law?
A ʌ (B v C) = (A ʌ B) v (A ʌ C)
A v (B ʌ C) = (A v B) ʌ (A v C)
A ʌ (B ʌ C) = (A ʌ B) ʌ (A ʌ C)
A ʌ (B v C) = (A v B) v (A v C)
How can expressions be simplified using Association Law?
(A ʌ B) ʌ C = A ʌ (B ʌ C) = A ʌ B ʌ C
(A v B) v C = A v (B v C) = A v B v C
How can expressions be simplified using Commutation Law?
A v B = B v A
A ʌ B = B ʌ A
How can expressions be simplified using Double Negation Law?
¬¬A = A
What is the purpose of a D-type flip flop?
To store the value of a single bit
When is the stored value in a D-type flip flop updated?
On the rising edge of the clock signal
Which logic gates are used in the logic circuit of a D-type flip flop?
4 NAND gates
What two inputs are taken in the logic gate of a D-type flip flop?
Control signal
Clock
What are adders?
Logic circuits which add together the number of inputs which are True
What two inputs are taken in the logic gate of a half adder?
A
B
What two outputs are produced in the logic gate of a half adder?
Sum
Carry
Which logic gates are used in the logic circuit of a half adder?
AND
XOR
What values are output by a half adder when both A & B are false?
Sum is False
Carry is False
What values are output by a half adder when A is True and B is False?
Sum is True
Carry is False
What values are output by a half adder when A is False and B is True?
Sum is True
Carry is False
What values are output by a half adder when both A & B are True?
Sum is False
Carry is True
What three inputs are taken in the logic gate of a full adder?
A
B
Carry (in)
What two outputs are produced in the logic gate of a full adder?
Sum
Carry (out)
Which logic gates are used in the logic circuit of a full adder?
2 XOR gates
2 AND gates
OR gate
