Java Reference
In-Depth Information
to count. A refinement of the tally system is to make groups of five ele-
ments by drawing a diagonal line for each fifth unit. The tally system does
not require numerical symbols. The ancient Egyptians used the tally sys-
tem to count from 1 to 9. Roman numerals probably derived from the tally
system since we can detect in some Roman numerals, the vertical and di-
agonal traces. In the system of Roman numerals there is no symbol for
zero, the digits have no positional value, and some digits require more
than one symbol. These factors make Roman numerals difficult to use.
The Hindu-Arabic system of numbers was introduced into Europe dur-
ing the 14th and 15th centuries. These numerals are used in a counting
scheme in which the value of each digit is determined by its column posi-
tion, for example, the number
4573
consists of 4 one-thousand units, plus 5 one-hundred units, plus 7 ten-units,
plus3singleunits.Thetotalvalueisobtainedbyaddingthecolumnweights
of each unit.
Binary numbers
The computers built in the United States during the early 1940s used deci-
mal numbers to store data and to perform arithmetic operations. In 1946,
John von Neumann observed that computing machinery would be easier to
build and would be more reliable if the electronic circuits were based on
two states, labeled ON and OFF, and that these two states could be repre-
sented by the digits 1 and 0. A system of numbers of only two digits is called
the
binary system
. With binary numbers, the two states of an electronic
cell are made to correspond to the digits 0 and 1.
Incidentally...
John von Neumann, who was of Hungarian descent, insisted that his
lastnameshouldbepronounced“fonNoiman”.In1930,hewasinvited
to be a visiting lecturer at Princeton University. He later became one
of the original six professors at Princeton's Institute for Advanced
Study and Research; Albert Einstein was one of the other five. In 1946,
von Neumann published a paper in collaboration with Arthur Burks
and Herman Goldstein. The paper, titled “A Preliminary Discussion of
the Logical Design of an Electronic Computing Instrument”, turned
out to be a perfect blueprint for building a computer. For this reason,
the modern-day digital computer is described as a von Neumann ma-
chine.
