Java Reference
In-Depth Information
1 = one
10 = ten
100 = hundred
1000 = thousand
In Arabic numbers the almost-magical symbol 0 does not correspond
to any unit-amount, but is used as a place-holder in a multi-column
scheme. All modern number systems, including decimal, hexadecimal,
and binary, are positional. The digits in the decimal number 2497 have the
following positional weights:
2000 ———- 2 thousand units
400 ———- 4 hundred units
+
90 ———- 9 ten units
7 ———- 7 units
_____
2497
or also
2*10
3
+4*10
2
+9*10
1
+7*10
0
= 2497
(Recall that 10
1
= 10 and 10
0
=1)
Computer Number Systems
ThecomputersbuiltintheUnitedStatesduringtheearly1940soperatedon
decimal numbers. However, in 1946 von Neumann, Burks, and Goldstine
published a seminal paper titled
Preliminary Discussion of the Logical
Design of an Electronic Computing Instrument.
In it they state:
“In a discussion of the arithmetic organs of a computing machine
one is naturally led to a consideration of the number system to be
adopted. In spite of the long-standing tradition of building digital
machines in the decimal system, we must feel strongly in favor of
the binary system for our device.”
Inthispapertheauthorsalsoconsiderthepossibilityofacomputingdevice
thatusesbinary-codeddecimalnumbers,calledBCD.Theideaisdiscarded
in favor of a pure binary encoding with the argument that binary numbers
aremorecompact.LaterinthischapteryouwillseethatBCDnumbersare
sometimesusedtoday.Nevertheless,thevonNeumanncomputermodelis
essentially a binary machine.
Radix or base
Inanypositionalnumbersystemtheweightofeachcolumnisdetermined
bythetotalnumberofsymbolsintheset,includingzero.Thisiscalledthe
