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Binary and Logic Lesson 3 - Denary to Binary

Last updated 10 months ago
14 questions

Learning Objectives

1: Understand the binary system
2: Know how to convert Denary to Binary


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

Recap: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 Denary?

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
1

How do you turn a Denary number into Binary?

  1. If your number can be subtracted by the heading number, put a 1. Else, put a 0.
  2. Start from the left-most bit. Can your denary number be substracted by that heading number?
  3. Continue with the next binary header to the right.
  4. Write the binary headings: 128 64 32 16 8 4 2 1
1

Guided Practice:
What is 67 as a 8-bit Binary number?

1

What is 8 in 8-bit binary?

1

What is 32 in 8-bit binary?

1

What is 72 in 8-bit binary?

1

What is 135 in 8-bit binary?

1

What is 127 in 8-bit binary?

1

What is 255 in 8-bit binary?

1

What is 31 in 8-bit binary?

1

What is 0 in binary?

1

Challenge:
With "8-bits" our highest value bit header is 128.
What do you think our next bit value would be if we had 9 bits?

1

Challenge:
If we only had "4-bits" - how many unique numbers can we make?

0

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

Screenshot your progress.