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
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 Binary?
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
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
How do you Convert a Binary number to a Denary Number?
Write the Binary number underneath each heading.
Add up all the headings where there is a "1" underneath it.
Write the Headings for each Binary digit (128 64 32 16 8 4 2 1)
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?
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
3 Bits | arrow_right_alt | 2 Numbers: 0 and 1 |
1 Bit | arrow_right_alt | 4 Numbers: 0 to 3 |
9 Bits | arrow_right_alt | 8 Numbers: 0 to 7 |
8 Bits | arrow_right_alt | 16 Numbers: 0 to 15 |
2 Bits | arrow_right_alt | 256 Numbers: 0 to 255 |
4 Bits | arrow_right_alt | 512 Numbers: 0 to 511 |
Go onto this link: https://learncomputing.org/binary#
Click on "Choose Quiz"
Click "GCSE"
then choose binary to denary.
Screenshot your progress.
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
What is 8 in binary?