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Binary and Logic Lesson 2 - Binary to Denary

Last updated 10 months ago
18 questions

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.
1

What is Binary?

1

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
1

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

  1. Write the Headings for each Binary digit (128 64 32 16 8 4 2 1)
  2. Write the Binary number underneath each heading.
  3. Add up all the headings where there is a "1" underneath it.
1

Guided Practice:
Convert 10000001 into denary

1

Guided Practice 2:
Convert 01001010 into denary

1

Convert 10000101 into denary

1

Convert 00001111 into denary

1

Convert 00101010 into denary

1

Convert 00000001 into denary

1

Convert 11111111 into denary

1

Convert 11100000 into denary

1

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

1

What is 01101011 in denary?

1

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

1

How many DIFFERENT numbers can be made with 8 bits?

1

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

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

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
0

What is 8 in binary?