Computer Number Systems

Because humans are complex creatures we use the base 10 system of decimal which is a fairly simple, yet still a complex system of counting, but it suites our needs fairly well. Computers count in very different ways than humans because computers are... well, morons. They can only perform the simplest of calculations using the base 2 system. However, because computers are so unbelievably fast, it's okay for them to use the base 2 system. If you don't understand what I'm talking about, don't worry. The following chart is used mainly by computer people, thus it's pointless.

Binary - Or base 2. There are only two numbers in binary, 0 and 1. Because computers use a sequence of switches that can be on or off (also called a bit), base 2 works very well for them. Math in base 2 is pathetically simple, but incredibly time consuming.

Octal - Or base 8. Uses the numbers 0 to 7. There are eight bits in a byte which is used very often in the computer field. (A bit is great, but it's too small to hold any useful data, thus the byte is used.) Math in octal is more complicated than decimal.

Decimal - Or base 10. Uses the numbers 0-9. I'm sure you're familiar with this system. Computers only display numbers in decimal, they actually do all their work in binary. Math is quite simple with this number system, although some may argue.

Hexadecimal - Or base 16. Uses the numbers 0-F. Yes, I said F. Because there are 16 values per place holder, five new numbers had to be created. Those numbers are A, B, C, D, E, and F (Original isn't it?). "A" has a value of 10, "B" is 11, and so on. We use this system in the computer field as a means of viewing lots of data much faster. As you can see in the chart below, the hexadecimal column is the smallest because it can handle more data per place holder. Very useful when looking at raw computer data. Math in hexadecimal is not very simple compared to decimal.


 

Computer Number Systems

Binary

Octal

Decimal

Hexadecimal

00000000

000

000

00

00000001

001

001

01

00000001

001

001

01

00000010

002

002

02

00000011

003

003

03

00000100

004

004

04

00000101

005

005

05

00000110

006

006

06

00000111

007

007

07

00001000

010

008

08

00001001

011

009

09

00001010

012

010

0A

00001011

013

011

0B

00001100

014

012

0C

00001101

015

013

0D

00001110

016

014

0E

00001111

017

015

0F

00010000

020

016

10

00010001

021

017

11

00010010

022

018

12

00010011

023

019

13

00010100

024

020

14

00010101

025

021

15

00010110

026

022

16

00010111

027

023

17

00011000

030

024

18

00011001

031

025

19

00011010

032

026

1A

00011011

033

027

1B

00011100

034

028

1C

00011101

035

029

1D

00011110

036

030

1E

00011111

037

031

1F

00100000

040

032

20

00100001

041

033

21

00100010

042

034

22

00100011

043

035

23

00100100

044

036

24

00100101

045

037

25

00100110

046

038

26

00100111

047

039

27

00101000

050

040

28

00101001

051

041

29

00101010

052

042

2A

00101011

053

043

2B

00101100

054

044

2C

00101101

055

045

2D

00101110

056

046

2E

00101111

057

047

2F

00110000

060

048

30

00110001

061

049

31

00110010

062

050

32

00110011

063

051

33

00110100

064

052

34

00110101

065

053

35

00110110

066

054

36

00110111

067

055

37

00111000

070

056

38

00111001

071

057

39

00111010

072

058

3A

00111011

073

059

3B

00111100

074

060

3C

00111101

075

061

3D

00111110

076

062

3E

00111111

077

063

3F

01000000

100

064

40

01000001

101

065

41

01000010

102

066

42

01000011

103

067

43

01000100

104

068

44

01000101

105

069

45

01000110

106

070

46

01000111

107

071

47

01001000

110

072

48

01001001

111

073

49

01001010

112

074

4A

01001011

113

075

4B

01001100

114

076

4C

01001101

115

077

4D

01001110

116

078

4E

01001111

117

079

4F

01010000

120

080

50

01010001

121

081

51

01010010

122

082

52

01010011

123

083

53

01010100

124

084

54

01010101

125

085

55

01010110

126

086

56

01010111

127

087

57

01011000

130

088

58

01011001

131

089

59

01011010

132

090

5A

01011011

133

091

5B

01011100

134

092

5C

01011101

135

093

5D

01011110

136

094

5E

01011111

137

095

5F

01100000

140

096

60

01100001

141

097

61

01100010

142

098

62

01100011

143

099

63

01100100

144

100

64

01100101

145

101

65

01100110

146

102

66

01100111

147

103

67

01101000

150

104

68

01101001

151

105

69

01101010

152

106

6A

01101011

153

107

6B

01101100

154

108

6C

01101101

155

109

6D

01101110

156

110

6E

01101111

157

111

6F

01110000

160

112

70

01110001

161

113

71

01110010

162

114

72

01110011

163

115

73

01110100

164

116

74

01110101

165

117

75

01110110

166

118

76

01110111

167

119

77

01111000

170

120

78

01111001

171

121

79

01111010

172

122

7A

01111011

173

123

7B

01111100

174

124

7C

01111101

175

125

7D

01111110

176

126

7E

01111111

177

127

7F

10000000

200

128

80

10000001

201

129

81

10000010

202

130

82

10000011

203

131

83

10000100

204

132

84

10000101

205

133

85

10000110

206

134

86

10000111

207

135

87

10001000

210

136

88

10001001

211

137

89

10001010

212

138

8A

10001011

213

139

8B

10001100

214

140

8C

10001101

215

141

8D

10001110

216

142

8E

10001111

217

143

8F

10010000

220

144

90

10010001

221

145

91

10010010

222

146

92

10010011

223

147

93

10010100

224

148

94

10010101

225

149

95

10010110

226

150

96

10010111

227

151

97

10011000

230

152

98

10011001

231

153

99

10011010

232

154

9A

10011011

233

155

9B

10011100

234

156

9C

10011101

235

157

9D

10011110

236

158

9E

10011111

237

159

9F

10100000

240

160

A0

10100001

241

161

A1

10100010

242

162

A2

10100011

243

163

A3

10100100

244

164

A4

10100101

245

165

A5

10100110

246

166

A6

10100111

247

167

A7

10101000

250

168

A8

10101001

251

169

A9

10101010

252

170

AA

10101011

253

171

AB

10101100

254

172

AC

10101101

255

173

AD

10101110

256

174

AE

10101111

257

175

AF

10110000

260

176

B0

10110001

261

177

B1

10110010

262

178

B2

10110011

263

179

B3

10110100

264

180

B4

10110101

265

181

B5

10110110

266

182

B6

10110111

267

183

B7

10111000

270

184

B8

10111001

271

185

B9

10111010

272

186

BA

10111011

273

187

BB

10111100

274

188

BC

10111101

275

189

BD

10111110

276

190

BE

10111111

277

191

BF

11000000

300

192

C0

11000001

301

193

C1

11000010

302

194

C2

11000011

303

195

C3

11000100

304

196

C4

11000101

305

197

C5

11000110

306

198

C6

11000111

307

199

C7

11001000

310

200

C8

11001001

311

201

C9

11001010

312

202

CA

11001011

313

203

CB

11001100

314

204

CC

11001101

315

205

CD

11001110

316

206

CE

11001111

317

207

CF

11010000

320

208

D0

11010001

321

209

D1

11010010

322

210

D2

11010011

323

211

D3

11010100

324

212

D4

11010101

325

213

D5

11010110

326

214

D6

11010111

327

215

D7

11011000

330

216

D8

11011001

331

217

D9

11011010

332

218

DA

11011011

333

219

DB

11011100

334

220

DC

11011101

335

221

DD

11011110

336

222

DE

11011111

337

223

DF

11100000

340

224

E0

11100001

341

225

E1

11100010

342

226

E2

11100011

343

227

E3

11100100

344

228

E4

11100101

345

229

E5

11100110

346

230

E6

11100111

347

231

E7

11101000

350

232

E8

11101001

351

233

E9

11101010

352

234

EA

11101011

353

235

EB

11101100

354

236

EC

11101101

355

237

ED

11101110

356

238

EE

11101111

357

239

EF

11110000

360

240

F0

11110001

361

241

F1

11110010

362

242

F2

11110011

363

243

F3

11110100

364

244

F4

11110101

365

245

F5

11110110

366

246

F6

11110111

377

247

F7

11111000

370

248

F8

11111001

371

249

F9

11111010

372

250

FA

11111011

373

251

FB

11111100

374

252

FC

11111101

375

253

FD

11111110

376

254

FE

11111111

377

255

FF

You may wonder why I only counted up to 256 (don't forget 0). Well 256 is a very common number in the computer field because it is a natural multiple of 2 (the base computers use). 256 is 2 to the 8th power (8 bits in a byte). Got it?

See also the ASCII Chart for more information.

Pointless