SLR 15 - BOOLEAN LOGIC Flashcards
What is the truth table for AND gates?
A | B | P
————
0 | 0 | 0
————
0 | 1 | 0
————
1 | 0 | 0
————
1 | 1 | 1
What is the truth table for OR gates?
A | B | P
————
0 | 0 | 0
————
0 | 1 | 1
————
1 | 0 | 1
————
1 | 1 | 1
What is the truth table for NOT gates?
0 | 1
——-
1 | 0
What is the truth table for XOR gates?
A | B | P
————
0 | 0 | 0
————
0 | 1 | 1
————
1 | 0 | 1
————
1 | 1 | 0
What is the notation for conjunction (AND)?
What is the notation for disjunction (OR)?
v
What is the notation for negation (NOT)?
¬
What is the notation for exclusive disjunction (XOR)?
⊻
What is the order of operations?
- brackets
- NOT
- AND
- OR/XOR
What is De Morgan’s 1st law?
¬ (A v B) = ¬ A ^ ¬ B
What is De Morgan’s 2nd law?
¬ (A ^ B) = ¬ A v ¬ B
X ^ 0
0
X ^ ¬ X
0
X v X
X
X ^ 1
X
X v 0
X
X v ¬ X
1
X ^ X
X
X v 1
1
¬ ¬ X
X
What is commutative law?
X ^ Y = Y ^ X
X v Y = Y v X
What is associative rule?
X ^ (Y ^ Z) = (X ^ Y) ^ Z
X v (Y v Z) = (X v Y) v Z
What is distributive rule?
X ^ (Y v Z) = (X ^ Y) V (X v Z)
(X v Y) ^ (W v Z) = (X ^ W) v (X ^ Z) v (Y ^ W) V (Y ^ Z)
What is absorption rule?
X v (X ^ Y) = X
X ^ (X v Y) = X
What are the rules when drawing and using a karnaugh map?
- order of numbers = 00, 01, 11, 10 (only 1 digit changes at a time)
- groups have to contain 1/2/4/8 1s
- boxes can overlap
- boxes can wrap around the map
