Number Systems

DECIMAL, BINARY, HEXADECIMAL NUMBER SYSTEMS

	Base	Symbols	# of Symbols	Place Values
DECIMAL	10	0 to 9	10	1000, 100, 10, 1
BINARY	2	0 and 1	2	16, 8, 4, 2, 1
HEXADECIMAL	16	0 to 9, A to F	16	4096, 256, 16, 1

Thanks to the zero, every position has a value (the Hindu-Arabic positional system). This is the concept of positional notation. Positional notation means that the value of a digit in a number depends not only on its own intrinsic value but also on its location in the number. When you see the number 2363, you are actually calculating (2 x 10³) + (3 x 10²) + (6 x 10¹) + (3 x 10⁰).
 

Next, some examples of the base-10, base-2, and base-16 number systems:

DEC BIN 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 8 1000 8 9 1001 9 10 1010 A

DEC BIN HEX 11 1011 B 12 1100 C 13 1101 D 14 1110 E 15 1111 F 16 10000 10 17 10001 11 18 10010 12 19 10011 13 20 10100 14 21 10101 15

DEC BIN HEX 22 10110 16 23 10111 17 24 11000 18 25 11001 19 26 11010 1A 27 11011 1B 28 11100 1C 29 11101 1D 30 11110 1E 31 11111 1F 32 100000 20 etc.!

Notice that the hex values for numbers larger than decimal 15 can be figured directly from the binary: just group them by fours and translate into hex.

The binary scheme uses only the two "BInary digiTS" (called "bits"): "0" and "1" to represent information in a computer.

These two-state devices are organized into groups called "bytes," each of which contains a fixed number of these devices, usually eight (the octal number system is based on 8 symbols: 0 to 7). Many programs store integers in 2 bytes or 16 bits. But the computer system is basically binary, so that everything has to be translated. We humans, with our ten figures, use the decimal system with 10 symbols: 0 to 9.

In the example below, the relays marked "1" are used, whereas those marked "0" are not. Here's how to translate a binary number scheme into a decimal one:

32 + 0 + 8 + 4 + 0 + 0 = 44 total in the decimal number system.

In other words: 101100₂ = 44₁₀

The RGB value is a code that specifies the amount of Red, Green, and Blue in the color (#rrggbb). For example, white is specified as 255 255 255. The hexadecimal (base 16) version of the RGB code is the code you use when you type in your color choices in an HTML page. White is specified as FF FF FF (FF₁₆ is the hexadecimal equivalent of decimal 255₁₀).

#F0 F8 FF 240 248 255 Alice Blue	#FA EB D7 250 235 215 Antique White	#7F FF D4 127 255 212 Aquamarine	#F0 FF FF 240 255 255 Azure	#F5 F5 DC 245 245 220 Beige	#FF E4 C4 255 228 196 Bisque	#00 00 00 0 0 0 Black	#FF EB CD 255 235 205 Blanched Almond	#00 00 FF 0 0 255 Blue
#8A 2B E2 138 43 226 Blue Violet	#A5 2A 2A 165 42 42 Brown	#DE B8 87 222 184 135 Burlywood	#5F 9E A0 95 158 160 Cadet Blue	#7F FF 00 127 255 0 Chartreuse	#D2 69 1E 210 105 30 Chocolate	#FF 7F 50 255 127 80 Coral	#64 95 ED 100 149 237 Cornflower Blue	#FF F9 DC 255 248 220 Cornsilk
#00 FF FF 0 255 255 Cyan	#00 00 8B 0 0 139 Dark Blue	#00 8B 8B 0 139 139 Dark Cyan	#B8 86 0B 184 134 11 Dark Goldenrod	#00 64 00 0 100 0 Dark Green	#A9 A9 A9 169 169 169 Dark Grey	#BD B7 6B 189 183 107 Dark Khaki	#8B 00 8B 139 0 139 Dark Magenta	#55 6B 2F 85 107 47 Dark Olive Green
#FF 8C 00 255 140 0 Dark Orange	#99 32 CC 153 50 204 Dark Orchid	#8B 00 00 139 0 0 Dark Red	#E9 96 7A 233 150 122 Dark Salmon	#8F BC 8F 143 188 143 Dark Sea Green	#48 3D 8B 72 61 139 Dark Slate Blue	#2F 4F 4F 47 79 79 Dark Slate Gray	#00 CE D1 0 206 209 Dark Turquoise	#94 00 D3 148 0 211 Dark Violet
#FF 14 93 255 20 147 Deep Pink	#00 BF FF 0 191 255 Deep Sky Blue	#69 69 69 105 105 105 Dim Grey	#1E 90 FF 30 144 255 Dodger Blue	#B2 22 22 178 34 34 Firebrick	#FF FA F0 255 250 240 Floral White	#22 8B 22 34 139 34 Forest Green	#DC DC DC 220 220 220 Gainsboro	#F8 F8 FF 248 248 255 Ghost White
#FF D7 00 255 215 0 Gold	#DA A5 20 218 165 32 Goldenrod	#00 FF 00 0 255 0 Green	#AD FF 2F 173 255 47 Green Yellow	#BE BE BE 190 190 190 Grey	#F0 FF F0 240 255 240 Honeydew	#FF 69 B4 255 105 180 Hot Pink	#CD 5C 5C 205 92 92 Indian Red	#FF FF F0 255 255 240 Ivory
#FF F6 8F 255 246 143 Khaki	#E6 E6 FA 230 230 250 Lavender	#FF F0 F5 255 240 245 Lavender Blush	#7C FC 00 124 252 0 Lawn Green	#FF FA CD 255 250 205 Lemon Chiffon	#AD D8 E6 173 216 230 Light Blue	#F0 80 80 240 128 128 Light Coral	#E0 FF FF 224 255 255 Light Cyan	#EE DD 82 238 221 130 Light Goldenrod
#D3 D3 D3 211 211 211 Light Gray	#90 EE 90 144 238 144 Light Green	#FF B6 C1 255 182 193 Light Pink	#FF A0 7A 255 160 122 Light Salmon	#20 B2 AA 32 178 170 Light Sea Green	#87 CE FA 135 206 250 Light Sky Blue	#84 70 FF 132 112 255 Light Slate Blue	#77 88 99 119 136 153 Light Slate Gray	#B0 C4 DE 176 196 222 Light Steel Blue
#FF FF E0 255 255 224 Light Yellow	#32 CD 32 50 205 50 Lime Green	#FA F0 E6 250 240 230 Linen	#FA FA D2 250 250 210 Lt Goldenrod Yello	#FF 00 FF 255 0 255 Magenta	#B0 30 60 176 48 96 Maroon	#66 CD AA 102 205 170 Medium Aquamarine	#00 00 CD 0 0 205 Medium Blue	#BA 55 D3 186 85 211 Medium Orchid
#93 70 DB 147 112 219 Medium Purple	#3C B3 71 60 179 113 Medium Sea Green	#7B 68 EE 123 104 238 Medium Slate Blue	#48 D1 CC 72 209 204 Medium Turquoise	#C7 15 85 199 21 133 Medium Violet Red	#00 FA 9A 0 250 154 Med Spring Green	#191970 25 25 112 Midnight Blue	#F5 FF FA 245 255 250 Mint Cream	#FF E4 E1 255 228 225 Misty Rose
#FF E4 B5 255 228 181 Moccasin	#FF DE AD 255 222 173 Navajo White	#00 00 80 0 0 128 Navy Blue	#FD F5 E6 253 245 230 Old Lace	#6B 8E 23 107 142 35 Olive Drab	#FF A5 00 255 165 0 Orange	#FF 45 00 255 69 0 Orange Red	#DA 70 D6 218 112 214 Orchid	#EE E8 AA 238 232 170 Pale Goldenrod
#98 FB 98 152 251 152 Pale Green	#AF EE EE 175 238 238 Pale Turquoise	#DB 70 93 219 112 147 Pale Violet Red	#FF EF D5 255 239 213 Papaya Whip	#FF DA B9 255 218 185 Peach Puff	#CD 85 3F 205 133 63 Peru	#FF C0 CB 255 192 203 Pink	#DD A0 DD 221 160 221 Plum	#B0 E0 E6 176 224 230 Powder Blue
#A0 20 F0 160 32 240 Purple	#FF 00 00 255 0 0 Red	#BC 8F 8F 188 143 143 Rosy Brown	#41 69 E1 65 105 225 Royal Blue	#8B 45 13 139 69 19 Saddle Brown	#FA 80 72 250 128 114 Salmon	#F4 A4 60 244 164 96 Sandy Brown	#2E 8B 57 46 139 87 Sea Green	#FF F5 EE 255 245 238 Seashell
#A0 52 2D 160 82 45 Sienna	#87 CE EB 135 206 235 Sky Blue	#6A 5A CD 106 90 205 Slate Blue	#C6 E2 FF 198 226 255 Slate Gray	#FF FA FA 255 250 250 Snow	#00 FF 7F 0 255 127 Spring Green	#46 82 B4 70 130 180 Steel Blue	#D2 B4 8C 210 180 140 Tan	#D8 BF D8 216 191 216 Thistle
#FF 63 47 255 99 71 Tomato	#40 E0 D0 64 224 208 Turquoise	#EE 82 EE 238 130 238 Violet	#D0 20 90 208 32 144 Violet Red	#F5 DE B3 245 222 179 Wheat	#FF FF FF 255 255 255 White	#F5 F5 F5 245 245 245 White Smoke	#FF FF 00 255 255 0 Yellow	#9A CD 32 154 205 50 Yellow Green