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Hexadecimal. Binary Made Easier. Quick Recap. Two different systems Computers use binary Binary is hard to read What is 1010001010111011??. Middle Ground. Need a system: Easier to read Converts easily to binary. Middle Ground. Need a system: Easier to read Converts easily to binary - PowerPoint PPT Presentation
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HexadecimalBinary Made Easier
Quick Recap
• Two different systems– Computers use binary– Binary is hard to read
• What is 1010001010111011??
System Base SymbolsUsed by humans?
Used in computers?
Decimal 10 0, 1, … 9 Yes No
Binary 2 0, 1 No Yes
Middle Ground
• Need a system:– Easier to read– Converts easily to binary
Middle Ground
• Need a system:– Easier to read– Converts easily to binary
• Hexadecimal – base 16
Hexdecimal
• Base 16– Each column is a power of 16:
= 4096 * 2 + 256 * 0 + 16 * 5 + 1 * 9= 8192 + 80 + 9205916 = 8281 in decimal
4096’s163
256’s162
16’s161
1’s160
2 0 5 9
13?
• How do we represent 13???
4096’s163
256’s162
16’s161
1’s160
13?
• How do we represent 13???– Use 0-9, A (10), B (11), C (12), D (13), E (14), F (15)
4096’s163
256’s162
16’s161
1’s160
D
16 Values
• Each column needs 16 values 0-15– Use 0-9, A (10), B (11), C (12), D (13), E (14), F (15)
= 256 * 1 + 16 * 14 + 1 * 9= 256 + 224 + 9= 489
4096’s163
256’s162
16’s161
1’s160
1 E 9
Counting
• Equivalent values : 1210 = 11002 = C16
Decimal Binary Hex
0 0 0
1 1 1
2 10 2
3 11 3
4 100 4
5 101 5
6 110 6
7 111 7
Decimal Binary Hex
8 1000 8
9 1001 9
10 1010 A
11 1011 B
12 1100 C
13 1101 D
14 1110 E
15 1111 F
Decimal Binary Hex
16 10000 10
17 10001 11
18 10010 12
19 10011 13
20 10100 14
21 10101 15
22 10110 16
23 10111 17
Conversion Among Bases
• The possibilities:
Hexadecimal
Decimal
Binary
Hex & Binary
• Each hex digit = 16 possible values• 4 binary digits = 16 possible values (24)• 1 hex digit = 4 binary digits
Decimal Binary Hex
0 0 0
1 1 1
2 10 2
3 11 3
4 100 4
5 101 5
6 110 6
7 111 7
Decimal Binary Hex
8 1000 8
9 1001 9
10 1010 A
11 1011 B
12 1100 C
13 1101 D
14 1110 E
15 1111 F
Binary -> Hex
• Break binary value into groups of 4:1001110100010110
Binary -> Hex
• Break binary value into groups of 4:1001110100010110
• Replace each group with 1 hex digit
Binary Hex
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F
Binary -> Hex
• Break binary value into groups of 4:1001110100010110 9 D 1 6
• Replace each group with 1 hex digit
10011101000101102 = 9D1616
Binary Hex Decimal
0000 0 0
0001 1 1
0010 2 2
0011 3 3
0100 4 4
0101 5 5
0110 6 6
0111 7 7
1000 8 8
1001 9 9
1010 A 10
1011 B 11
1100 C 12
1101 D 13
1110 E 14
1111 F 15
Hex -> Binary
• Replace each hex digit with 4 binarydigits:
• Ex: F2
F 2 1111 0010
F216 = 111100102
Binary Hex
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F
Hex Decimal
Use a tableDigits 0-FA = 10B = 11C = 12D = 13E = 14F = 15
4096’s163
256’s162
16’s161
1’s160
Hex Decimal
Use a tableDigits 0-FA = 10B = 11C = 12D = 13E = 14F = 15
4096’s163
256’s162
16’s161
1’s160
1 C 7
256 x 1 + 16 x 12 + 1 x 7 = 256 + 192 + 7
= 455
1C716 = 45510
Decimal Hex
Division / Multiplication methods:
Current Value Quotient Remainder
455 ÷ 16 28 7 7
28 ÷ 16 1 12 (C) C71 ÷ 16 0 1 1C7
Summary
• Hex is a bridge:– Easier for us– Still just binary for computers
System Base SymbolsUsed by humans?
Used in computers?
Decimal 10 0, 1, … 9 Yes No
Binary 2 0, 1 No Yes
Hex 16 0-9ABCDEF
No, butbetter than
binary
No, but easily translates to
binary
Colors
• Monitors make colors by mixing red/green/blue light:
• Typical 24 bits : 8 bits for each color– 28 = 256 possible values
Colors
• Hex Colors– Each color stored as 0-255– 8 bits– 2 hex digits
Web Colors
• Website colors often written in hex#RRGGBB– Two digits for red, two for green, two for blue
Black #000000 (0,0,0) White #FFFFFF (255,255,255) Red #FF0000 (255,0,0) Lime #00FF00 (0,255,0) Blue #0000FF (0,0,255) Yellow #FFFF00 (255,255,0) Cyan / Aqua #00FFFF (0,255,255)
