Binary and Logic Lesson 2 - Binary to Denary - Matthew Chau [Stoke] | Library

Learning Objectives
1: Understand the binary system
2: Know how to convert binary to denary
3: To be aware how the number of Bits can affect how many numbers you can make

For revision, use the BBC Bitesize link: https://www.bbc.co.uk/bitesize/guides/z26rcdm/revision/1

What is Binary?

In computing, we often use two systems to represent numbers: binary and denary. 

The binary system uses only two digits, 0 and 1 because computers only understand this.
While the denary system is the one we use every day, which includes the digits from 0 to 9. 

In denary, a number is represented with Units, Tens, hundreds, thousands  (Goes up by x10)
e.g. 1000 100 10 1

In binary, a number is represented with 1, 2, 4, 8, 16 .... (goes up by x2)
e.g. 128 64 32 16 8 4 2 1
Each Binary digit, is called a "bit".

E.g. The denary number 64 can be represented in binary (0s and 1s) as 01000000.

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Drag the numbers into the correct category. Can the number be a binary number or not?

32
16
1000
10010000
01000001
0
1
128

Can be a Binary Number
Cannot be a binary number

Example question:  
Convert the 8-bit binary number 10011010 into denary.

Step 1: Write the binary headings.
Headings for 8 bits:
128  64  32  16   8   4   2   1

Step 2: Put the binary number underneath
128  64  32  16   8   4   2   1
   1     0    0     1    1   0  1   0
Step 3: Add the heading values where there is a 1.
128  64  32  16   8   4   2   1
   1     0    0     1    1   0  1   0
= 128 + 16 + 8 + 2 
= 154 

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Guided Practice:
Convert 10000001 into denary

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Guided Practice 2:
Convert 01001010 into denary

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Convert 10000101 into denary

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Convert 00001111 into denary

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Convert 00101010 into denary

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Convert 00000001 into denary

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Convert 11111111 into denary

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Convert 11100000 into denary

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What is 01000000 in denary? (You can draw the table this time)

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What is 01101011 in denary?

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What is the largest denary number that can be represented with 8-bits?

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How many DIFFERENT numbers can be made with 8 bits?

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How many different numbers can be made with the following number of bits?

Draggable item		Corresponding Item
9 Bits		2 Numbers: 0 and 1
4 Bits		4 Numbers: 0 to 3
2 Bits		8 Numbers: 0 to 7
1 Bit		16 Numbers: 0 to 15
8 Bits		256 Numbers: 0 to 255
3 Bits		512 Numbers: 0 to 511

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Go onto this link: https://learncomputing.org/binary#
Click on "Choose Quiz"
Click "GCSE"
then choose binary to denary.

Screenshot your progress.

Reading for next lesson
How to convert a Denary number to Binary:
E.g. Convert 135 into Binary

Step 1: Write the binary headings.
Headings for 8 bits:
128  64  32  16   8   4   2   1

Step 2: Start from the left-most header. 
If the number can be subtracted, but a 1.
Else put a 0. 
Continue going right with the remainder.

135 - 128 = 7 (remaining)
128  64  32  16   8   4   2   1
    1
7 - 64 will be less than 0, so put a 0.
128  64  32  16   8   4   2   1
    1    0
7 - 32?  Put a 0.
128  64  32  16   8   4   2   1
    1    0     0
7 - 16?  Put a 0.
128  64  32  16   8   4   2   1
    1    0     0    0
7 - 8?  Put a 0.
128  64  32  16   8   4   2   1
    1    0     0    0    0
7 - 4 = 3 (remaining)
128  64  32  16   8   4   2   1
    1    0     0    0   0   1
3 - 2 = 1 (remaining)
128  64  32  16   8   4   2   1
    1    0     0    0   0   1    1

1 - 1 = 0 (remaining)
128  64  32  16   8   4   2   1
    1    0     0    0   0   1    1  1 


135 into Binary is 10000111

https://www.bbc.co.uk/bitesize/guides/z26rcdm/revision/3 

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Binary and Logic Lesson 2 - Binary to Denary

Binary and Logic Lesson 2 - Binary to Denary

Learning Objectives

What is Binary?

Drag the numbers into the correct category. Can the number be a binary number or not?

Example question:

Guided Practice:Convert 10000001 into denary

Guided Practice 2:Convert 01001010 into denary

Convert 10000101 into denary

Convert 00001111 into denary

Convert 00101010 into denary

Convert 00000001 into denary

Convert 11111111 into denary

Convert 11100000 into denary

What is 01000000 in denary? (You can draw the table this time)

What is 01101011 in denary?

What is the largest denary number that can be represented with 8-bits?

How many DIFFERENT numbers can be made with 8 bits?

How many different numbers can be made with the following number of bits?

Go onto this link: https://learncomputing.org/binary#Click on "Choose Quiz" Click "GCSE"then choose binary to denary.Screenshot your progress.

Reading for next lesson

How to convert a Denary number to Binary:

What is 8 in binary?

Learning Objectives

What is Binary?

What is Binary?

Drag the numbers into the correct category. Can the number be a binary number or not?

Example question:

How do you Convert a Binary number to a Denary Number?

Guided Practice:Convert 10000001 into denary

Guided Practice 2:Convert 01001010 into denary

Convert 10000101 into denary

Convert 00001111 into denary

Convert 00101010 into denary

Convert 00000001 into denary

Convert 11111111 into denary

Convert 11100000 into denary

What is 01000000 in denary? (You can draw the table this time)

What is 01101011 in denary?

What is the largest denary number that can be represented with 8-bits?

How many DIFFERENT numbers can be made with 8 bits?

How many different numbers can be made with the following number of bits?

Go onto this link: https://learncomputing.org/binary#Click on "Choose Quiz" Click "GCSE"then choose binary to denary.Screenshot your progress.

Reading for next lesson

How to convert a Denary number to Binary:

What is 8 in binary?

What is Binary?

How do you Convert a Binary number to a Denary Number?

Guided Practice:
Convert 10000001 into denary

Guided Practice 2:
Convert 01001010 into denary

Go onto this link: https://learncomputing.org/binary#
Click on "Choose Quiz"
Click "GCSE"
then choose binary to denary.

Screenshot your progress.

Guided Practice:
Convert 10000001 into denary

Guided Practice 2:
Convert 01001010 into denary

Go onto this link: https://learncomputing.org/binary#
Click on "Choose Quiz"
Click "GCSE"
then choose binary to denary.

Screenshot your progress.