1. 4. Computer Maths and Logic 4.2 Boolean Logic 4.2.3 Simplifying Boolean Expressions

2. Complex expressions can be constructed using the operators e.g. (A  B) (C + D), which is equivalent to writing (A xor not B) and (neither C nor D nor both). In the exam, you will not have to consider more than 3 inputs Complex Expressions

3. To evaluate a complex Boolean expression, break it down to smaller parts then use a truth table e.g. firstly (A  B): Complex Expressions

4. 1011 0101 0010 1100 (A  B)‏ BBA OutputIntermedi ate Inputs Complex Expressions

5. There’s a worksheet to help you evaluate the rest of the expression Draw similar truth tables for A + B and A B. Truth tables can be used as a means of checking if two expressions are equivalent. Complex Expressions

6. Complex expressions can often be reduced to simpler ones This is similar to work you have done in algebra in maths Look out for the following expressions which are always true Simplifying Expressions

7. A 0 = 0 A + 1 = 1 Simplifying Expressions

8. A 1 = A A + 0 = A Simplifying Expressions

9. A + A = A A A = A Simplifying Expressions

10. A B = B A A + B = B + A (the commutative law) ‏ Simplifying Expressions

11. A (B C) = (A B) C = A B C (the associative law) ‏ Simplifying Expressions

12. A + (B + C) = (A + B) + C = A + B + C (the associative law) ‏ Simplifying Expressions

13. A (B + C) = AB + AC (A + B) (A + C) = AA + AC + BA + BC (the distributive law) ‏ Verify these with truth tables Simplifying Expressions

14. A + A = 1 A A = 0 (De Max's laws) ‏ Simplifying Expressions

15. A + B = A B De Morgen's law Verify these with truth tables Simplifying Expressions

16. anything in brackets is done first is done before + Simplifying Expressions