Week 6 Numeracy skills
Here are a number of sites that explain how to convert between bases:
This is the best and most animated:
• binary 1 through to binary 7
The following act as additional examples and resources:
Everything in one place: http://www.golgotha.org.uk/useful/bases.html
Understanding Base 10
http://www.codemastershawn.com/library/tutorial/hex.bin.numbers.php
Decimal Notation
Zero
0
One
1
Two
2
Three
3
Four
4
Five
5
Six
6
Seven
7
Eight
8
Nine
9
Ten
1
0
Eleven 1
1
The base of a number is what you count up to before you indicate a digit in the second column. Trouble is, we only have the numerals 09 for digits as our language is based on base 10 numbering (maybe because we have ten fingers). When we're counting in base 16 we
use the letters a-f as notation for the remaining digits we need. The number eleven, for example, would be written as B. Counting to
seventeen in Base 16 looks like this:
Hex Notation
Zero
One
Two
Three
Four
Five
Six
Seven
Eight
Nine
Ten
Eleven
Twelve
Thirteen
Fourteen
Fifteen
Sixteen
1
Seventeen
1
Eighteen
1
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
0
1
2
1. Find the closest even product of 16 for your number.
2. Indicate the remainder using the table above.
* For instance, 72 divided by 16 is 4, or 64, which leaves a remainder of 8. To write 72 in hexadecimal notation you would write 48, "four
sixteens and eight remainder". Likewise to indicate the number 255 in hexadecimal you would write FF, because 15 sixteens are 240, so
there are 15 sixteens in the left column, which leaves a remainder of 15 in the right column.
Understanding Binary:
A base 2 8-bit
number system represented by the numeric values of 0 or 1, also known as ON or OFF, and the primary language that computers
communicate in. Below is an example of the maximum 8-bit value of 255, which is 11111111 in binary. To get this value add each
column, so 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255.
Value: 128
ON/OFF:
64
1
32
1
16
1
8
1
4
1
2
1
1
1
1
Below is another example of 10001101, which is 141 or 1 + 4 + 8 + 128.
Value: 128
ON/OFF:
64
1
32
0
16
0
8
0
4
1
2
1
1
0
1
Binary and hexadecimal conversions
http://www.computerhope.com/binhex.htm To convert a value from hexadecimal to binary, you
merely translate each hexadecimal digit into its 4-bit binary equivalent. Hexadecimal numbers have either and 0x prefix or an h suffix.
For example, the hexadecimal number:
0x3F7A
Translates into, Using the Binary chart and the below chart for Hex:
0011 1111 0111
1010
Decimal Hexadecimal Binary
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
http://www.ecawa.asn.au/home/jfuller/binary/binary7.htm
Example 1. Consider Binary: 1000100100110111 (a 16-bit Byte)
STEP 1 Break the Byte into 'quartets' - 1000 1001 0011 0111
STEP 2
Use the table above to covert each quartet to its Hex equivalent - 8937
Therefore ... 1000100100110111 = #8937
Understanding the Binary System http://pcnineoneone.com/howto/binary2
Understanding the Hexadecimal Number System
http://pcnineoneone.com/howto/hex1/
http://pcnineoneone.com/howto/hex2/
http://pcnineoneone.com/howto/hex_sidebar2/
HEX
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
00
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
01
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
02
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
03
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
04
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
05
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
06
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
07
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
08
128
129
130
Conversion Code - Chart (http://easycalculation.com/hex-converter.php)
DECIMAL
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
HEX
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
BINARY
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
Converter online:
http://www.yellowpipe.com/yis/tools/hex-to-rgb/color-converter.php