1. 4. 3 Boolean Algebra

Question 1

Logic Gate Diagrams and Truth Tables

Answer 1

Refer to images in word doc

Question 2

Karnaugh Maps

Answer 2

• Used to simplify Boolean expressions
• Always remember to go from left to right, 00 to 01 to 11 to 10
• The rule is we can only change a single digit at a time as shown below
• The rules about boxing in order to do the simplification are as follows
• Boxes must be rectangles or squares, no diagonal boxes, they must only contain 1’s
• Boxes must be as large as possible, boxes must be of 2^n (1, 2, 4, 8, 16 etc)
• Boxes can overlap, must have the smallest possible number of boxes, boxes can wrap around the map

Question 3

Example of Karnaugh Maps

Answer 3

• The simplification below results in B V C because they stay consistent
• Remember consistent 0’s use NOT (¬A), consistent 1’s use just the letter (A)
• Refer to word doc

Question 4

Simplifying Boolean Expressions

Answer 4

• De Morgan’s Law, Distribution, Association, Commutation and Double Negation
• Refer to image in word doc

Question 5

Logic Circuits- D-Type Flip Flops

Answer 5

• D-Type Flip Flops are a type of logic circuit which can store the value of one bit
• Two inputs, a control signal and a clock input
• Clock is a regular pulse generated by CPU
• This is used to coordinate the computers components
• Clock pulse rises and falls as shown in image below
• Output of a D-type flip flop can only change at a rising edge (start of a clock tick)
• A flip-flop is a basic unit of memory

Question 6

Adders

Answer 6

Adders are logic circuits which add together the number of inputs which are true and outputs the number in binary, two types Half and Full

Question 7

Half-Adders

Answer 7

• Half Adder has two inputs (A and B) two outputs (Sum and Carry)
• Circuit formed by two logic gates, AND and XOR

Question 8

Full-Adders

Answer 8

• Full Adder has an additional input allowing for carry in to be represented
• Circuit formed using two XOR gates, two AND gates and an OR gate (5 gates total)