Data Representation
Binary
Devices have two states 1 or 0.
Denary |
Binary |
0 |
0 |
1 |
001 |
2 |
010 |
3 |
011 |
4 |
100 |
5 |
101 |
6 |
110 |
7 |
111 |
8 |
1000 |
9 |
1001 |
10 |
1010 |
11 |
1011 |
12 |
1100 |
Binary is in Base 2.
For example 4 would be show as:
| 64 |
32 |
16 |
8 |
4 |
2 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
Teaching Ideas.
Activity.
Give 5 people a card with the numbers 1,2,4,8,16 on. Say a set of numbers and get the students to work out which numbers are needed to make that number.
Computer Science Unplugged.
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CD and Music- Reward good behaviour and working with choosing a winner each class that can bring in a CD to play next lesson.
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Little man computers
Maths.
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1000
104 = 10 x 10 x 10 x 10 = 10000
Binary
| 25 |
24 |
23 |
22 |
21 |
20 |
32 |
16 |
8 |
4 |
2 |
1 |
Base 8
Other.
Denary
Binary
ASCII - American Standard Code for Characters.
Hexadecimal
Bytes and Bits:
8 Bits = 1 Byte
4 Bits = 1 Nibble
Byte = 8 Bits
Kilobyte = 1024 Bits
Terabyte.
Petabyte.
Assembly Language consisted of:
ADD
SUB
MUL
DIV
PRNT
Denary to Binary
| Denary |
1024 |
512 |
256 |
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
29 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
53 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
1 |
74 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
555 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
752 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
|
|
|
|
|
|
|
|
|
|
|
|
Octal system Base 8.
| 83 |
82 |
81 |
80 |
512 |
64 |
8 |
1 |
|
|
|
|
4 |
0 |
7 |
3 |
Hexadecimal Base 16
| Denary |
Hexadecimal |
0 |
0 |
1 |
1 |
2 |
2 |
3 |
3 |
4 |
4 |
5 |
5 |
6 |
6 |
7 |
7 |
8 |
8 |
9 |
9 |
10 |
A |
11 |
B |
12 |
C |
13 |
D |
14 |
E |
15 |
F |
|
|
|
|
163 |
162 |
161 |
160 |
4096 |
256 |
16 |
1 |
Binary Addition
0 + 0 = 0 carry 0
0 + 1 = 1 carry 0
1 + 0 = 1 carry 0
1 + 1 = 0 carry 1
1 + 1 + 1 = 1 carry 1
Binary Addition
|
|
1 |
1 |
1 |
1 |
0 |
|
|
1 |
1 |
0 |
1 |
1 |
Total |
1 |
1 |
1 |
0 |
0 |
1 |
Carry |
1 |
1 |
1 |
1 |
0 |
|
Octal to denary
| Octal Number |
512 |
64 |
8 |
1 |
Denary Equivalent |
40738 |
4 |
0 |
7 |
3 |
(4x512) + (0x64)+ (7x8) +(3 x 1) =2048+0+56+3 = 210710 |
Hexadecimal to Denary
| Hexadecimal |
256 |
16 |
1 |
Denary Equivalent |
61016 |
6 |
1 |
0 |
(6x256)+ (1x 16) + (0x1) = 1536+16+0 = 155210 |
BIDMAS
Brackets
Indices
Division
Multiplication
Addition
Subtraction
Binary to Hexadecimal Conversion
Split Binary into sets of 4 numbers
Hexadecimal to Binary Conversion
| F (15) |
3 |
C(12) |
1111 |
0011 |
1100 |
Binary to Octal Conversion
Split into sets of 3 numbers
Octal to Binary Conversion
