Logic

3. Binary Logic

Binary logic is much the same as general logic, except it works on 1's and 0's. Given one or more binary inputs a logical output will result.

It is common practice to consider binary 1 to be 'True' and binary '0' to be 'False'.

There are only a few simple logic operations but they do lead to incredibly complex devices such as a CPU.

The logic operations are: NOT, AND, OR

Invert or NOT operation

This operation operates on a single input, let's call it input A to produce a single output Q

In English the rule is

"If A is True then the output Q is False, if the input A is False then the output Q is True"

So this operation produces an output that is opposite to the input

The shorthand way of writing this is Q = NOT A where 'A' is the input and 'Q' is the output.

It does not have to be A and Q, you could use any letter, but Q is a popular choice to describe a logic output.

The AND operation

This operation acts upon at least two inputs, say A, B to produce a single output Q.

In English, the rule is

"If both A and B are True then the output Q is also True, otherwise it is False".

The shorthand for this is Q = A AND B

The OR operation

Again, this needs at least two inputs A, B to produce a single output.

In English the rule is

"If either or both A, B are True then the output Q is also True."

The shorthand for this is Q = A OR B

The table below is a summary

Extra Fact:

There is one other popular logic operation called the 'Exclusive OR' but you do not need to know the details for this syllabus. But basically it says "If A OR B is true then the output is true, however is both of them are true at the same time, then the output is false"