07 Mar 2006
Great Inventions: Drawing the Numbers

The problem is to represent X number of things using symbols.
You can represent numbers by dots (unary system) and put down as many dots as X. That quickly becomes laborious and boring if you were to write down a large number.
Ancient Romans invented way to map numbers to symbols. If that system was still in wide use, solaris mpstat command would have produced an output like this:
CPU minf mjf xcal intr ithr csw icsw migr smtx srw syscl usr sys wt idl
- XVI I - CDLXXXIV CCCLXXXIV DXXII XXXV - - - DCCXVI X IV - LXXXV
- CDLXXXIV - - DXXX CDXXIX DLXXXIX XIII - - - MDLXXV IX IV - LXXXVII
- - - - DCCXCVI DCXCVII MCXXVIII XXVI - - - MMCCLXII V IV - XCI
- - - - DCCCXXX DCCXXIX MCCCXXXIII CCXIII - I - MMMCCCXLIII XXI V - LXXIV
- - - - DXXIX CDXXX DXXII IV - - - DCCCLXXII IV III - XCIII
- CXXVI - - CDLXXI CCCLXX CDLIII XXVII - - - DLXXXV VIII III - LXXXIX
- - - - DLXXIV CDLXXIV DCLXX V - - - MCCXXVI IV III - XCIII
- - - - DCCLXXXII DCLXXXII MCLXX XLV - - - MMCDXCI V IV - XCI
- - - - DCCCXXIII DCCXXIII MCCCLIII CLXXI - - - MMMCDLXV XVIII V - LXXVII
Luckily we had the "base" system where numbers are divided in the form of Symbol X base
n + Symbol X base
n-1 + ... + Symbol X base
0.
You just drop the
* basen repeaters and draw the symbols next to each other to get the graphical representation of a number.
CPU minf mjf xcal intr ithr csw icsw migr smtx srw syscl usr sys wt idl
0 16 1 0 484 384 522 35 0 0 0 716 10 4 0 85
0 484 0 0 530 429 589 13 0 0 0 1575 9 4 0 87
0 0 0 0 796 697 1128 26 0 0 0 2262 5 4 0 91
0 0 0 0 830 729 1333 213 0 1 0 3343 21 5 0 74
0 0 0 0 529 430 522 4 0 0 0 872 4 3 0 93
0 126 0 0 471 370 453 27 0 0 0 585 8 3 0 89
0 0 0 0 574 474 670 5 0 0 0 1226 4 3 0 93
0 0 0 0 782 682 1170 45 0 0 0 2491 5 4 0 91
0 0 0 0 823 723 1353 171 0 0 0 3465 18 5 0 77
The base system made the common cases easy: common cases are
compare two numbers,
remember and
write numbers,
add or subtract numbers.
Life would have been so difficult without the base representation; an early application of human interaction principle, made so much difference!
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