Lesson 25 Binary Recap/Intro

​AAQ Binary Recap/Intro

By Ryan Mordey

Binary is a base 2 number system that is used to process data by a computer.

All data processed by a digital device is converted into binary, this is the only data a device can process, as it is how the transistors function on the CPU.

Each transistor can have 2 states ON (1) or OFF (0)

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Binary

Binary to Denary

Each 1 or 0 in the binary sequence is given a base 2 number. This is how we convert it into denary (Human numerical system/base 10)

To make a denary number from our binary we place the 1's and 0's in the sequence into the above table. We then look at which values contain a 1. These values are added together to get a denary result.

Multiple Choice

What number base is used by binary?

• 2

• 10

• 5

• 4

Multiple Choice

What is meant by base 2?

• Base 2 means each number is ten times the number.

• Base 2 means that each number in the sequence goes up in twos.

• Base 2 means that each number has 2 added to it from the number before it.

• Base 2 means each number is twice as big as the number before.

Binary to Denary

Here is an example:

The largest number that can be made with 8 bits is 255, the smallest number is 0. We would know if its the largest number at it would all be 1's the smallest number would all be 0's.

Denary to Binary

We can reverse the process by drawing out the binary table and placing the numbers in the correct space to add up to the denary value:

Multiple Choice

Convert 11111111 from binary to denary

• 128
• 64
• 255
• 512

Multiple Choice

Convert the denary number 25 to binary:

• 000011010

• 000011001

• 000010101

• 000011100

Binary Logic

Represented by NOT A

Represented by A AND B

Represented by A OR B

We can then use Logic to manipulate the binary data or output in a transistor.

​A	​Output
​0	​1
​1	​0

​A	B​	Output
​0	0​	0​
​0	1​	1
1​	0​	1
​1	1​	1

​A	B​	Z​
​0	0​	0​
​0	1​	0​
1​	0​	0​
​1	1​	1​

Exclusively OR

Represented by A XOR B

There is additional logic you need to be aware of at Level 3 including Exclusively OR or XOR.

The word exclusive that only 1 input can be on, in order for the output to be on. If both A and B are on, the output would be off. It can only be one OR the other.

​A	B​	Output
​0	0​	0​
​0	1​	1
1​	0​	1
​1	1​	0

Match

Connect the correct truth table to the corresponding logic gate expression.

NOT A

A AND B

A OR B

A XOR B

• NOT A

• A AND B

• A OR B

• A XOR B

As all data that is processed through a computer is binary we use character sets with a standard numeric value for each character on the keyboard.

ASCII is one method that is used where each character has a 8 bit binary value, we can then work out the denary equivalent by converting binary to denary.

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ASCII

Multiple Choice

What is the purpose of ASCII?

• The purpose of ASCII is to provide a standard way to represent text in computers.
• ASCII is a programming language for web development.
• The purpose of ASCII is to enhance video quality.
• ASCII is used for image compression in computers.