How Computers Represent Data

As we discussed in class, computers store and process every type of data in numerical form. Here are some examples:

Images
 

Image (charlotte.jpg):

To see the same image, represented as numbers, click here. The first three lines of the file contain information about the image. In particular, this image is 200 pixels wide by 270 pixels high. The maximum pixel value is 255. From then on, every threesome of numbers indicates the red, green, and blue values of a pixel. The first pixel in the picture has the following values: red 207, blue 237, green 245. (White is red 255, blue 255, and green 255. Black is red 0, blue 0, and green 0.)

Sounds

Music, stored in sample.wav (Click on it to play it) (For more information about the recording, click here.) The same music, at half volume (half.wav) The same music, filtered to remove most of the lowest and highest tones (filter.wav) 
The first 0.01 second of sample.wav: The first 0.01 second of half.wav: The first 0.01 second of filter.wav:
Here are the numbers representing the first 1/100 of a second of sample.wav (each number represents the voltage of the audio wave at a particular time slice): Here are the same numbers for half.wav (notice the numbers are half the values at left): Here are the same numbers for filter.wav:

Click here to see the numbers for all three files in binary.

478
1393
1784
1580
903
196
-237
-640
-1293
-1771
-2123
-2688
-3361
-3827
-3727
-3446
-3275
-3694
-4156
-4524
-4601
-4404
-4025
-3518
-2919
-2373
-2111
-1818
-1295
-590
650
1618
2533
2935
3092
3395
4260
5265
6113
6826
7313
7536
7557
7497
7421
7131
6579
5728
4995
4722
4425
4268
4416
4826
4819
4181
3368
2885
2613
2002
1188
811
731
671
350
-12
-139
135
186
-5
-392
-761
-1029
-1206
-965
-672
-233
135
342
474
342
-267
-919
-1214
-1263
-1432
-1255
-736
-357
-136
126
260
325
50
-338
-707
-1169
-1666
-2442
-2923
-3153
-3373
-3673
-4084
-4091
-3457
-2806
-2491
-2566
-2604
-2447
-1946
-1198
-607
-326
-393
-359
-581
-998
-1619
-2210
-2687
-2842
-2544
-2381
-2555
-2484
-2134
-1681
-1604
-1744
-1830
-2013
-2107
-1938
-1760
-1536
-1407
-1345
-1041
-677
-564
-379
-314
15
546
700
1161
1749
2287
2887
3523
3990
4155
4102
3452
2362
1641
1300
921
268
-286
-511
-577
-677
-901
-1199
-1604
-1960
-2354
-2580
-2929
-3195
-2957
-2168
-1337
-769
-94
358
843
1037
822
673
759
1094
1418
1503
1793
2451
2816
3253
3462
3208
2617
1836
1092
574
453
183
-230
-735
-1252
-2144
-3281
-4088
-4325
-4167
-3822
-3755
-3801
-3825
-3703
-3729
-3748
-3724
-3662
-3411
-3067
-2305
-1078
194

239
696
892
790
451
98
-119
-320
-647
-886
-1062
-1344
-1681
-1914
-1864
-1723
-1638
-1847
-2078
-2262
-2301
-2202
-2013
-1759
-1460
-1187
-1056
-909
-648
-295
325
809
1266
1467
1546
1697
2130
2632
3056
3413
3656
3768
3778
3748
3710
3565
3289
2864
2497
2361
2212
2134
2208
2413
2409
2090
1684
1442
1306
1001
594
405
365
335
175
-6
-70
67
93
-3
-196
-381
-515
-603
-483
-336
-117
67
171
237
171
-134
-460
-607
-632
-716
-628
-368
-179
-68
63
130
162
25
-169
-354
-585
-833
-1221
-1462
-1577
-1687
-1837
-2042
-2046
-1729
-1403
-1246
-1283
-1302
-1224
-973
-599
-304
-163
-197
-180
-291
-499
-810
-1105
-1344
-1421
-1272
-1191
-1278
-1242
-1067
-841
-802
-872
-915
-1007
-1054
-969
-880
-768
-704
-673
-521
-339
-282
-190
-157
7
273
350
580
874
1143
1443
1761
1995
2077
2051
1726
1181
820
650
460
134
-143
-256
-289
-339
-451
-600
-802
-980
-1177
-1290
-1465
-1598
-1479
-1084
-669
-385
-47
179
421
518
411
336
379
547
709
751
896
1225
1408
1626
1731
1604
1308
918
546
287
226
91
-115
-368
-626
-1072
-1641
-2044
-2163
-2084
-1911
-1878
-1901
-1913
-1852
-1865
-1874
-1862
-1831
-1706
-1534
-1153
-539
97		 271
807
1114
1016
524
-182
-873
-1414
-1834
-2267
-2817
-3458
-4036
-4374
-4417
-4285
-4207
-4370
-4783
-5256
-5520
-5392
-4893
-4231
-3657
-3301
-3088
-2801
-2232
-1334
-260
735
1455
1888
2200
2624
3301
4198
5133
5897
6376
6588
6632
6586
6446
6140
5616
4918
4200
3661
3432
3502
3718
3865
3777
3404
2820
2163
1557
1061
665
330
24
-241
-434
-523
-518
-477
-485
-610
-864
-1184
-1457
-1564
-1434
-1080
-596
-129
173
215
-17
-449
-937
-1328
-1508
-1442
-1171
-787
-384
-29
238
398
421
281
-27
-469
-977
-1480
-1941
-2365
-2769
-3136
-3396
-3457
-3272
-2890
-2447
-2093
-1894
-1785
-1616
-1255
-686
-43
467
676
538
138
-373
-865
-1269
-1571
-1767
-1841
-1775
-1576
-1298
-1026
-838
-767
-796
-873
-949
-986
-960
-857
-675
-436
-184
36
204
345
510
741
1041
1380
1730
2105
2557
3134
3810
4463
4916
5017
4724
4120
3366
2615
1956
1404
943
559
252
21
-164
-358
-619
-973
-1406
-1865
-2276
-2557
-2627
-2423
-1934
-1221
-427
276
756
977
1004
956
935
986
1104
1279
1528
1880
2331
2809
3170
3264
3004
2422
1663
922
354
6
-208
-467
-945
-1718
-2707
-3694
-4428
-4759
-4714
-4477
-4271
-4226
-4318
-4422
-4436
-4360
-4273
-4224
-4134
-3805
-3050
-1846
-391