Boolean & K-Maps

Question 1

identity law

Answer 1

1 ^ A = A
0 v A = 0

Question 2

Null law

Answer 2

0 ^ A = 0
1 v A = 1

Question 3

Idempotent law

Answer 3

A ^ A = A
A v A = A

Question 4

inverse law

Answer 4

A ^ ¬A = 0
A v ¬A = 1

Question 5

commutative law

Answer 5

A ^ B = B ^ A
A v B = B v A

Question 6

associative law

Answer 6

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

Question 7

distributive law

Answer 7

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

Question 8

absorption law

Answer 8

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

Question 9

de morgan’s law

Answer 9

¬(A ^ B) = ¬A v ¬B
¬(A v B) = ¬A ^ ¬B

Question 10

how to find DNF or SOP from K-Maps

Answer 10

• look for groups of 1sa
• group size 2^n only
• based on inputs determine a product (AND) term which evaluates to 1

Question 11

how to find CNF or POS from K-Maps

Answer 11

• look for groups of 0s
• group size 2^n only
• based on inputs determine a product (AND) term which evaluates to 0

Question 12

quine-mcluskey method

Answer 12

1. tabulate expression & find pairs (where only one expression is different) - ¬A^B^C^D and ¬A^B^C^¬D give ¬A^B^C
2. create a new table with terms left from the previous stage & find pairs & combine
3. left with only terms that cannot be simplified further
4. create a matrix & circle each x that is alone in a column
5. put a square around any x that is in the same row as a circle x
6. the terms with a square x are the terms of our minimised expression