1. GCSE
OCR
Computing
A451
Binary logic
2-1-2 Computing hardware 6

2. Objectives
Explain why data is represented in computer systems in binary form
Understand and produce simple logic diagrams using the operations NOT, AND and OR
Produce a truth table from a given logic diagram

3. Why is binary so important?
Reflected light
Magnetic polarisation
Power
Trapped electrons

4. Why is binary so important?
Fundamentally computers are electronic and can decide between two states – true or false, on or off, presence or absence of current and translate this into the binary representation of 1 or 0

5. Binary Logic
As computers use transistors and capacitors to store binary data we can wire them together to make simple logical calculations
These simple circuits are known as logic gates
There are three fundamental gates you know need to know about:
NOT gate
AND gate
OR gate

6. Boolean Algebra: P = NOT A
Binary Logic – NOT gate
If 0 is input it outputs 1
If 1 is input it outputs 0
INPUT A
OUTPUT P
Boolean Algebra: P = NOT A A P 1
Logic Diagram
Truth Table

7. Boolean Algebra: P = A AND B
Binary Logic – AND gate
If both inputs are 1 then the output is 1
Otherwise the output is 0 A B P 1
INPUT A B
OUTPUT P
Boolean Algebra: P = A AND B
Logic Diagram
Truth Table

8. Boolean Algebra: P = A OR B
Binary Logic – OR gate
If either input is 1 then the output is 1
Otherwise the output is 0 A B P 1
INPUT A B
OUTPUT P
Boolean Algebra: P = A OR B
Logic Diagram
Truth Table

9. Order of Precedence Brackets NOT AND OR
When combining logic gates, there are certain rules to follow to ensure you complete the circuits correctly.
A bit like in maths where you need to use BIDMAS, with logic gates you need to know the Order of precedence
It is:
Brackets NOT AND OR

10. Combining logic gates
We can string logic gates together to make more complex circuits
INPUT A
OUTPUT R P A B
R = A AND B
P = NOT R 1
Boolean Algebra:
P = NOT (A AND B)

11. Combining logic gates
We can string logic gates together to make more complex circuits
OUTPUT R
INPUT A
OUTPUT P
INPUT A A B
R = A AND B
P = NOT R 1
Boolean Algebra:
P = NOT (A AND B)

12. Combining logic gates
We can string logic gates together to make more complex circuits
OUTPUT R
INPUT A
OUTPUT P
INPUT A A B
R = A AND B
P = NOT R 1
Boolean Algebra:
P = NOT (A AND B)

13. Increasing the number of inputs
What happens if we had three inputs. How many possible combinations are there now?
32 = 2 x 2 x 2 = 8 possible input combinations
OUTPUT P
INPUT A B C R
Boolean Algebra:
P = (A AND B) OR C

14. Combining logic gates A B C R = A AND B P = R OR C Boolean Algebra:
OUTPUT P
INPUT A
INPUT B
INPUT C R
Boolean Algebra:
P = (A AND B) OR C

15. Combining logic gates A B C R = A AND B P = R OR C 1 Boolean Algebra:1
OUTPUT P
INPUT A
INPUT B
INPUT C R
Boolean Algebra:
P = (A AND B) OR C

16. Practise makes perfect
In the exam you will need to be able to do the following:
Complete truth tables from a logic diagram
Produce simple logic diagrams from Boolean algebra
An excellent site to practise is: