Binary Logic & Truth Tables

Question 1

General Logic & Binary Logic

Answer 1

General Logic
Generally speaking you use logic to work out whether something is true or false.

Binary Logic
Binary logic is similar to general logic except it uses 1’s and 0’s.
Consider now that a binary 1 would be True
Consider now that a binary 0 would be False

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

These are the logic operations you NEED TO KNOW!!! So MEMORISE THEM as you may get a question on this and you will not have access to the descriptions below

Question 2

The NOT operation

Answer 2

The NOT operation, also called the ‘Invert’ operation

This operation produces an output that is the opposite of the input.
Where a 1 is input, a 0 is the output
Where a **0 **is input, a 1 is the output

Question 3

The AND operation

Answer 3

This operation relies on at least two inputs to produce a single output.

If BOTH A AND B is true, then the output is true
Where a 1 AND a 1 are the inputs, the output is 1 - True AND True = True
Where a 0 AND a 1 are the inputs, the output is 0 – False AND True = False
Where a 1 AND a 0 are the inputs, the output is 0 – True AND False = False
Where a 0 AND a 0 are the inputs, the output is 0 – False AND False = False

Question 4

The OR operation

Answer 4

This operation relies on at least two inputs to produce a single output

Where either A OR B or BOTH are true, the output is also TRUE, otherwise it is FALSE

Where a 0 OR a 0 are the inputs, the output is 0 - False OR False = False

Where a 0 OR a 1 are inputs, the output is 1 – False OR True = True

Where a 1 OR a 0 are the inputs, the output is 1 – True OR False = True

Where a 1 OR a 1 are the inputs, the output is 1 – True OR True = True

Question 5

The XOR operation

Answer 5

The XOR gate states that if one, and only one of the inputs is true, then the output is true. If both inputs are false or if both inputs are true, a false is the result.

A way to remember XOR is simply “one or the other but not both”

The XOR operation
Where a 1 and a 1 are the inputs, the output is 0 – True XOR True = False

Where a 1 and a 0 are the inputs, the output is 1 – True XOR False = True

Where a 0 and a 1 are inputs, the output is 1 – False XOR True = True

Where a 0 and a 0 are the inputs, the output is 0 - False XOR False = False

Question 6

Truth Tables

Answer 6

Question 7

Truth Tables 2

Answer 7