Applied Mathematic
(Preliminary General 1)
Converting
Bits and Bytes
Stage 6 - Year 11
Press Ctrl-A
©G Dear 2010 – Not to be sold/Free to use
1
Converting Bits and Bytes
Whatever you do when you work
You will be using computers at some point
You will come across the terms
Bits and Bytes.
It’s unlikely you will need to do
any calculations
But an understanding of what
it all means is useful.
End of
Slide
2
Binary Number System – Computer Talk
Computers talk in 1’s and 0’s called bits.
1 byte = 8 bits
27 26 25 2 4 23 22 21 20
128 64 32 16 8 4 2 1
Nibble 2
Place
Values
Nibble 1
Decimal Numbers
0 to 255
End of
Slide
3
Converting Bits and Bytes
1

1
1
1
1
1
1
1
1
27 26 2 5 24 23 22 21 20
128 64 32 16 8 4 2 1
2
3
4
5
6
7
8

9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
Click on any number.
[5 second display]
End of
Slide
4
Converting Bytes to Hexadecimal
1 byte = 8 bits
23 22 21 20 23 22 21 20
8
4 2 1 8 4 2 1
Nibble 2
Nibble 1
Hexadecimal Number
0 to FF
End of
Slide
5
Converting Bits and Bytes
Hexadecimal Numbers
Dec 0
Hex 0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
Dec 8
Hex 8
9 10 11 12 13 14 15
9 A B C D E F
End of
Slide
6
Converting Bytes to Hexadecimal
Add the numbers with a 1 under them.
1280 641 322 163 84
Dec
Hex0 0 0 1 02 03 14
Decimal = 1 + 8 = 9
Dec8 8 4 9 210 111 8
12
Hex0 8 0 9 0A 0B 1C
0
Hexadecimal = 09
4
5
0
5
2
6
0
6
71
71
13
4
D
0
14
2 15
1
E
0 F1
8+1=9
Press
End of
Slide
7
Converting Bytes to Decimal & Hexadecimal
Add the numbers with a 1 under them.
1280 641 322 16
Dec
3 84
Hex0 0 0 1 02 03 14
Decimal = 8 + 4 + 1
Dec8 8 4 9 210 111 8
12
Hex0 8 0 9 0A 0B 1C
4
5
1
5
62
60
71
71
= 13
13
4 14
2 15
1
D
1 E
0 F1
0
8 + 4 + 1 = 13 = D
Hexadecimal = 0D
Press
End of
Slide
8
Converting Bytes to Decimal & Hexadecimal
Add the numbers with a 1 under them.
1280 641 322 16
Dec
3 84
Hex0 0 0 1 12 13 04
Decimal = 32+ 16 + 4
Dec8 8 4 9 210 111 12
8
Hex0 8 0 9 1A 1B 0C
2+1=3
Hexadecimal = 35
4
5
1
5
62 71
60 71
+ 1 = 55
13
4 14
2 15
1
D
1 E
0 F1
4+1=5
Press
End of
Slide
9
Converting Bytes to Decimal & Hexadecimal
Add the numbers with a 1 under them.
1280 641 322 163 84 4
Dec
5 62
Hex1 0 0 1 12 13 14 0
5 61
Decimal = 128 + 32+ 16 + 8 + 2 =
Dec8 8 4 9 210 111 8
12 13
4 14
2
Hex1 8 0 9 1A 1B 1C 0
D E
1
71
70
186
15
1
F0
8 + 2 + 1 = 11 = B
8 + 2 = 10 = A
Hexadecimal = BA
Press
End of
Slide
10
Converting Bytes to Decimal & Hexadecimal
Add the numbers with a 1 under them.
Dec 0
Hex 0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
Dec 8
Hex 8
9 10 11 12 13 14 15
9 A B C D E F
End of
Slide
11