Boolean logic

What are the main features of boolean logic?

• It is a branch of mathematics

• created by George Boole

• The values are binary so either True or False

• 4 Main logic operators(in order of operation):

• NOT

• AND

• OR

• XOR

What is the algebraic and alternative symbols of AND?

Algebraic: ^ e.g. A ^ B

Alternative: . e.g A . B

What is the algebraic and alternative symbols of OR?

Algebraic: v e.g A v B

Alternative: + e.g. A + B

What is the algebraic symbol of XOR?

Algebraic: ⊕ e.g A ⊕ B

What is the algebraic and alternative symbols of NOT?

Algebraic: ¬ e.g ¬A

Alternative: Ā e.g Ā

What are the four algebraic operation names?

NOT = negation

AND = conjunction

OR = disjunction

XOR = exclusive disjunction

What is the difference between ¬(A ^ B) and ¬A ^ ¬B

• The first one requires you to work out A ^ B first as it is in brackets then invert the 0 and 1.

• The second one requires you to work out NOT A and NOT B first then add them.

What can you use to simplify boolean expressions?

Karnough maps

What are the 6 rules of K maps

• Grouping should be a power of 2

• no diagonal groups

• they should be as large as possible

• henceforth meaning fewest number of groups

• overlapping allowed

• wrapping around allowed

What is an adder and half adder?

• Half adder - basic digital circuit used two add two singe bit numbers - has two outputs and two inputs - sum and carry. (carry is the 1 carried over)

• Adder - extension of the half adder to add three bits. - two outputs - three inputs

Why do CPU’s not have half adders at the start?

Because that would require two molds to make full and half adders, so its cheaper just to make one.

What is the logic gate for a half adder?

What is the truth table for a half adder?