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hexadecimal

the hexadecimal numeral system differs from the decimal system by having 16 digits rather than 10:

hex dec
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
A 10
B 11
C 12
D 13
E 14
F 15

when there is more than one digit, these are multiplied by 16, 256, 4096 and so on rather than 10, 100, 1000:

hex dec
00 0
04 4
08 8
0F 15
10 16
11 17
12 18
13 19
20 32
30 48
40 64

hex to decimal

for example, take hexadecimal number AA:

          2nd digit -\   /- 1st digit
                     A   A
 16^1*10 = 16*10 = 160 + 10 = 170

now for hexadecimal number 4C5F:


      3rd digit -\    /- 2nd digit
 4th digit -\    |    |    /- 1st digit
            4    C    5    F
            |    |    |    |
            |    |    |    15 =        15 =    15 +
            |    |    \16^1*5 =   16 * 5  =    80
            |    \--- 16^2*12 =  256 * 12 =  3072
            \--------- 16^3*4 = 4096 * 4  = 16384
                                           -------
                                          = 19551

decimal to hex

if it's less than 16, just memorize the table at the top of this document.

otherwise find the power of 16 that is closest to the number you want to convert, but no larger than the number. then divide, and take the remainder. divide the remainder with the previous power of 16, until the divider is 1.

for example, for the decimal number 220:

220 ÷ 16 = 13 (r = 12)    D
 12 ÷  1 = 12 (stop here) C

= DC

now for decimal number 69420:

69420 ÷ 65536 =  1 (r = 3884)  1
 3884 ÷  4096 =  0 (r = 3884)  0
 3884 ÷   256 = 15 (r =   44)  F
   44 ÷    16 =  2 (r =   12)  2
   12 ÷     1 = 12 (stop here) C

= 10F2C

bitmask

a bitmask is a value that actually represents a set of individual binary bits to be toggled, some of which may be grouped to form small binary numbers. these are used by adding up the value of each bit and converting the result to hex. in macros, these are shown in decimal.

bit binary decimal
bit 7 1000 0000 128
bit 6 0100 0000 64
bit 5 0010 0000 32
bit 4 0001 0000 16
bit 3 0000 1000 8
bit 2 0000 0100 4
bit 1 0000 0010 2
bit 0 0000 0001 1

for example, to turn bits 7 and 5 on, and put 110 (decimal 6) in bits 1 to 3:

bit binary decimal
bit 7 1... .... 128
bit 6 .0.. .... 0
bit 5 ..1. .... 32
bit 4 ...0 .... 0
bit 3 .... 1... 8
bit 2 .... .1.. 4
bit 1 .... ..0. 0
bit 0 .... ...0 0

added together, the resulting binary is 1010 1100, which converts to hex as AC and to decimal as 172.

hex to decimal table

hex 0 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
10 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
20 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
30 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
40 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79
50 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
60 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111
70 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127
80 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143
90 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159
A0 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175
B0 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191
C0 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207
D0 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223
E0 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239
F0 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255