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
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.
What is Denary?
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
How do you turn a Denary number into Binary?
Start from the left-most bit. Can your denary number be substracted by that heading number?
Continue with the next binary header to the right.
If your number can be subtracted by the heading number, put a 1. Else, put a 0.
Write the binary headings: 128 64 32 16 8 4 2 1
Guided Practice:
What is 67 as a 8-bit Binary number?
What is 8 in 8-bit binary?
What is 32 in 8-bit binary?
What is 72 in 8-bit binary?
What is 135 in 8-bit binary?
What is 127 in 8-bit binary?
What is 255 in 8-bit binary?
What is 31 in 8-bit binary?
What is 0 in binary?
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?
Challenge:
If we only had "4-bits" - how many unique numbers can we make?
Go onto this link: https://learncomputing.org/binary#
Click on "Choose Quiz"
Click "GCSE"
then choose either Denary to Binary
Screenshot your progress.