1.4.3 - Boolean Algebra

What are the types of logic gates

Symbol

AND - Conjunction - ^

OR - Disjunction - v

NOT - Negation - ¬

XOR - Exclusive Disjunction - v with a line under it

What is a Karnaugh map

Draw one

A way of mapping out the effect variables have when they are true/ false

What are the simplifying laws

De Morgan

Distribution

Associating

Commutation

Double Negation

What is de morgans law

Breaking the negative and then changing the operator between two literals

What is distribution

A and B or A and C = A and (C or B)

A or B and A or C = A or (B and C)

What is association

Getting rid of/ adding brackets

Commutation

A and B is equal to B and A

Double negation

Double negative = positive

What are the logic circuits you should know

D-type flips flops

Half adders

Full adders

What is the D-type flip flop

Has two inputs - clock pulse (Used to coordinate components of the CPU) and a control signal

Output will change at a rising edge - the start of a clock tick

The image updates the value of Q whenever the clock ticks (Rising edge) The value of is the stored value in the image.

A flip-flop is a basic unit of memory and set of flip-flops can be combined together to create registers

What is an adder

A logic circuit which adds together the number of inputs which are true and outputs the number in binary

There are two adder circuits - half and full

What is an half adder

Two inputs - A and B

Two outputs - Sum and Carry

Circuit is formed from just two logic gates AND, XOR

What is a full adder

Similar to half adder but has an additional input allowing for a carry in to be represented.

The carry in allows the full adder to be chained together as the result from the last will be CARRIED IN