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

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

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

(A  B)‏ BBA OutputIntermedi ate Inputs Complex Expressions

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

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

A 0 = 0 A + 1 = 1 Simplifying Expressions

A 1 = A A + 0 = A Simplifying Expressions

A + A = A A A = A Simplifying Expressions

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

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

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

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

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

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

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