Logic

Question 1

NOT logic gate

Answer 1

▶o

Question 2

AND logic gate

Answer 2

D

Question 3

OR logic gate

Answer 3

)> (concave and pointy ver of and)

Question 4

XOR logic gate

Answer 4

) )> (same as or with added curved line in front)

Question 5

AND boolean symbol

Question 6

OR boolean symbol

Answer 6

∨

Question 7

XOR boolean symbol

Answer 7

v with line underneath

Question 8

NOT boolean symbol

Answer 8

¬

Question 9

order of precedence for boolean expressions

Answer 9

Brackets
NOT
AND
OR and XOR

Question 10

Double Negation

Answer 10

If there are two nots in front of a letter they can be erased

¬¬A = A

Question 11

Commutation

Answer 11

The order of letters around an operator can be changed (remember the NOT symbol stays with the letter)

A v ¬B = ¬B v A

Question 12

Association

Answer 12

If a long expression contains only one operator, letters can be reordered, and brackets can be added or taken away

A ^ B ^ ¬C = ( A ^ ¬C) ^ B

Question 13

Distribution

Answer 13

If there is more than one operator, letters outside brackets can be “distibruted” to the letters inside the brackets

A v ( B ^ C ) = ( A v B) ^ ( A v C )

Question 14

De Morgan’s Law

Answer 14

If there is a NOT outside of a bracket, it can be added to the letters inside, but the operator must change

¬( A v B) = ¬A ^ ¬B

Question 15

What is a Karnaugh Map

Answer 15

• A summary version of a truth table used to simplify logic expressions
• Can have up to 4 inputs (2 per axis)

Question 16

How are inputs written on the axis of a Karnaugh map

Answer 16

not in binary number order. They are written like this :

00
01
11
10

so that only 1 bit changes at a time.

Question 17

How Karnaugh maps correspond to a truth table

Answer 17

Each row of a truth table matches a square of a karnaugh map

Question 18

How Karnaugh maps correspond to a logical expression

Answer 18

• look at each part of the expression
• find the value of that part (such as AvB) and fill in a 1 in all squares that match that condition.

Question 19

How to mark groups in a karnaugh map

Answer 19

• Must have 1, 2, 4, or 8 1s.
• Squares or rectangles only
• Can overlap
• no 1s must be left out
• groups as big as possible

Question 20

How to use karnaugh map to create logical expression

Answer 20

• Describe each group, connect using AND operator.