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1

Basic rules of Boolean Algebra

1. A + 0 = A 7. A . A = A
2. A + 1 = 1 8. A .~A = 0
3. A. 0 = 0 9. ~~A = A
4. A .1 = A 10. A + AB = A
5. A + A = A 11. A + (~A)B = A + B
6. A + ~A = 1 12. (A + B)(A + C) = A + BC

2

Application of Boolean Algebra:

Simplification means fewer gates for
the same function.

3

In karnaugh map, rules for groups:

Groups of 1 only.
1. they must be horizontal or vertical react, or squares. not L or anything, not diagonal.
2. groups can only contain 2^n members. 2,4,8...
3. groups should be as large as possible, remember they can overlap.
4. u will have to roll the table to see the group, even if members are at the end of the table its fine as long as they the adjacent cells.

4

Adjacent cells:

Cells who differ by only one bit in karnaugh map. like 000 and 001 are adjacent.

5

Universal gates

nand , nor. Any circuit can be implemented by nand or nor alone.

6

XOR gate as and, or?

Y = A(~B) + (~A)B