every time another power of two is reached, for example, 2, 4, 8, and so on; in the dec-
imal system, another place is added every time a power of 10 is reached, for example,
10, 100, 1000, and so on.
Computers use this simple number system primarily because binary information
is easy to store. A computer’s CPU (Central Processing Unit) and memory are made up
of millions of “switches” that are either off or on—the symbols 0 and 1 represent
those switches, respectively—and are used in the calculations and programs. The two
numbers are simple to work with mathematically within the computer. When a person
enters a calculation in decimal form, the computer converts it to binary, solves it, and
then translates that answer back to decimal form. This conversion is easy to see in the
following table:
Decimal Binary
00
11
210
311
4 100
5 101
6 110
7 111
8 1000
9 1001
10 1010
11 1011
12 1100
13 1101
14 1110
15 1111
16 10000
17 10001
18 10010
19 10011What was the Turing machine?
In 1937, while working at Cambridge University, English mathematician Alan Mathi-
son Turing (1912–1954) proposed the idea of a universal machine that could perform
mathematical operations and solve equations. This machine would use a combination 361