1. Component 1 – 2A, B, C Binary Logic
Mr Petford

2. Learning Intentions
Learning Intention: To simplify Boolean Algebra expressions using Boolean Identities
Developing
Draw truth tables for Boolean Identities including AND and OR
Secure
Simplify Boolean expressions using Boolean identities

3. Binary Logic – Not Gate Logic Diagram If 0 is input it outputs 1
Boolean Algebra: P = A’
P = A
Logic Diagram

4. Binary Logic – AND Gate Logic Diagram
If both inputs are 1 then the output is 1
Otherwise the output is 0
INPUT A B
OUTPUT P
Boolean Algebra: P = A.B
P = AB
P = AxB
Logic Diagram

5. Boolean Algebra: P = A + B
Binary Logic – OR Gate
If either input is 1 then the output is 1
Otherwise the output is 0
INPUT A B
OUTPUT P
Boolean Algebra: P = A + B
Logic Diagram

6. Boolean Algebra: P = A ⊕ B
Binary Logic – XOR Gate
If either input is 1 then the output is 1
UNLESS! Both are 1!
Otherwise the output is 0
INPUT A B
OUTPUT P
Boolean Algebra: P = A ⊕ B
Logic Diagram

7. Boolean Algebra: P = A+B
Binary Logic – OR Gate
NOR stands for NOT OR
If either input is 1 then the output is 0
Otherwise the output is 1 A B P 1
INPUT A B
OUTPUT P
Boolean Algebra: P = A+B
Logic Diagram

8. Algebra Laws - identity
The Sum(OR) of anything and Zero is the same as the original
The sum (OR)of anything and One is always 1.
The Sum(OR) of Anything and its self is the same as the original
The Sum(OR) of anything and its opposite is always 1. 1

9. Algebra Laws - identity
Just as there are four Sum (OR) identities There are also 4 multiplicative identities Which can be seen below

10. Algebra Laws - identity
To simplify…

11. Finding the value
The easiest way to simplify the Boolean expression is to use factorising.
X = A.B + A. B What can you see that is common across the equation?

12. Finding the value X = A.B + A. B
What can you see that is common across the equation? A.
To factorise we move A to be in Brackets
X = A.(B + B )

13. Finding the value
X = A.B + A. B
What can you see that is common across the equation? A.
To factorise we move A to be in Brackets
X = A.(B + B )
So what does B + B mean? B or Not B Lets put that into a logic diagram.. What do you think this will do? B

14. Finding the value
X = A.(B + B ) So what does B + B mean? B or Not B Lets put that into a logic diagram.. What do you think this will do?
It will always be true! Which means it will always be on! Which means it will always be 1. Therefore.. X = A.(1) We know that A and 1 is always going to be 1 because: B
A = 1 1 1

15. Finding the value
It will always be true! Which means it will always be on! Which means it will always be 1. Therefore.. X = A.(1) We know that A and 1 is always going to be 1 because:
X = A To recap: X = A.B + A. B X = A.(B + B ) X = A.(1) X=A
A = 1 1

16. Workbook
Complete section 2b Q1

17. Binary Bits Each 1 or 0 is called a bit - 1
8 bits is called a byte – e.g
4 bits is called a nibble – e.g. 1010
In the same way as a kilometre is meters, we can group together bytes and call it a kilobyte
8 bits = 1 byte
1024 bytes = 1 kilobyte
1024 kilobytes = 1 megabyte
1024 megabyte = 1 gigabyte
1024 gigabytes = 1 terabyte
To be able to convert between Binary, Denary, and Hexadecimal
To be able to perform Binary Addition
To understand the advantages of Hexadecimal over Binary
To understand the relationships between Base 2, 10, and 16
How do you convert from Binary to Denary?
How do you convert from

18. Workbook
Complete section 2b Q2