Control Data 3100 Reference Manual page 189

DECIMAL/BINARY POSITION TABLE
Decimal
Number
Largest Decimal of
Integer
Digits
Binary
Largest Decimal Fraction
Req'd*
Digits
1
1
.5
3 2 .75
7 3 .875
15 1 4 .937 5
31
5
.968 75
63 6 .984 375
127 2 7 .992 187 5
255 8 .996 093 75
511 9
.998 046 875
1 023 3 10 .999 023 437 5
2 047 11 .999 511 718 75
4 095
12
.999 755 859 375
8 191 13 .999 877 929 687 5
16 383 4 14 .999 938 964 843 75
32 767 15
.999 969 482 421 875
65 535 16 .999 984 741 210 937 5
131 071 5 17 .999 992 370 605 468 75
262 143 18
.999 996 185 302 734 375
524 287
19
.999 998 092 651 367 187 5
1 048 575 6 20 .999 999 046 325 683 593 75
2 097 151 21 .999 999 523 162 841 796 875
4 194 303 22 .999 999 761 581 420 898 437 5
8 388 607 23
.999 999 880 790 710 449 218 75
16 777 215 7 24
.999 999 940 395 355 244 609 375
33 554 431 25 .999 999 970 197 677 612 304 687 5
67 108 863 26 .999 999 985 098 838 806 152 343 75
134 217 727 8 27 .999 999 992 549 419 403 076 171 875
268 435 455
28
.999 999 996 274 709 701 538 085 937 5
536 870 911 29 .999 999 998 137 354 850 769 042 968 75
1 073 741 823 9 30 .999 999 999 068 677 425 384 521 484 375
2 147 483 647 31
.999 999 999 534 338 712 692 260 742 187 5
4 294 967 295 32 .999 999 999 767 169 356 346 130 371 093 75
8 589 934 591 33 .999 999 999 883 584 678 173 065 185 546 875
17 179 869 183 10
34
.999 999 999 941 792 339 086 532 592 773 437 5
34 359 738 367 35 .999 999 999 970 896 169 543 266 296 386 718 75
68 719 476 735 36 .999 999 999 985 448 034 771 633 148 193 359 375
137 438 953 471 11 37 .999 999 999 992 724 042 385 816 574 096 679 687 5
274 877 906 943 38 .999 999 999 996 362 021 192 908 287 048 339 843 75
549 755 813 887
39
.999 999 999 998 181 010 596 454 143 524 169 921 875
1 099 511 627 775 12 40 .999 999 999 999 090 505 298 227 071 762 084 960 937 5
2 199 023 255 551 41 .999 999 999 999 545 252 649 113 535 881 042 480 468 75
4 398 046 511 103
42
.999 999 999 999 772 626 324 556 767 940 521 240 234 375
8 796 093 022 207 43 .999 999 999 999 886 313 162 278 383 970 260 620 117 187 5
17 592 186 044 415 13
44
.999 999 999 999 943 156 581 139 191 985 130 310 058 593 75
35 184 372 088 831 45 .999 999 999 999 971 578 290 569 595 992 565 155 029 296 875
70 368 744 177 663
46
.999 999 999 999 985 789 145 284 797 996 282 577 514 648 437 5
140 737 488 355 327 14
47
.999 999 999 999 992 894 572 642 398 998 141 288 757 324 218 75
*Larger numbers within a digit group should be checked for exact number of decimal digits required.
Examples of use:
1.
Q. What is the largest decimal value that can be expressed by 36 binary digits?
A.68,719,476,735.
2.
Q. How many decimal digits will be required to express a 22-bit number?
A. 7 decimal digits.
C-2