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

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

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

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

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

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

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

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

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

Algebra Laws - identity To simplify…

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?

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 )

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

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

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

Workbook Complete section 2b Q1

Binary Bits Each 1 or 0 is called a bit - 1 8 bits is called a byte – e.g. 1110 0101 4 bits is called a nibble – e.g. 1010 In the same way as a kilometre is 1000 meters, we can group together 1024 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

Workbook Complete section 2b Q2