Java Reference
In-Depth Information
1.3 Binary Representation of Numbers
It is important to understand the fact that a computer can store only zeros and ones.
Consider the integer 423. It is equal to 4
10
0
. This is known as
base 10
representation
because every digit is between 0 and 9. Similarly, there is base 2 represen-
tation that uses only 2 digits: 0 and 1. This is also referred to as the
binary
representation
of the number. For example, the binary number 01010010 represents the decimal number
0
10
2
+2
10
1
+3
·
·
·
2
0
= 82.
There is also an easy algorithm for converting a decimal integer to a binary number.
Consider the decimal integer 134. The conversion algorithm keeps dividing the number by
2 and records the remainders.
134 /2 = 67 remainder 0
67 / 2 = 33 remainder 1
33 / 2 = 16 remainder 1
16 /2 = 8 remainder 0
8/2=4remainder0
4/2=2remainder0
2/2=1remainder0
add a 1
The binary number is created by starting with the number 1 and then taking the re-
mainders in reverse order. For example, the decimal number 134 is equal to the binary
number 10000110. To verify our work, we can try to convert the number back to a decimal
number. It will be equal to: 1
2
7
+1
2
6
+0
2
5
+1
2
4
+0
2
3
+0
2
2
+1
2
1
+0
·
·
·
·
·
·
·
·
2
0
= 134.
Sometimes, data that is stored in computers is represented using hexadecimal numbers.
These are numbers in base 16. Table 1.2 shows the hexadecimal digits. The first 10 digits
are the same as the decimal digits. Then the letters A-F are used to represent the numbers
10-15. Consider the hexadecimal number 4F1A. Since a hexadecimal digit takes 4 bits to
represent, the number will be 16 bits or 2 bytes long. To convert it into a binary number,
we can just use Table 1.2 as a reference and convert every digit individually. In binary, the
number will be: 0100 1111 0001 1010. Since the hexadecimal representation of a number is
much shorter than the binary representation, it is often used to represent binary data, such
as main memory addresses.
·
2
7
+0
·
2
6
+0
·
2
5
+0
·
2
4
+0
·
2
3
+1
·
2
2
+1
·
2
1
+0
·
1.4 Software Creation and Types of Software
Software is usually written by
software programmers
using a
programming language
,such
as Java or C. It is then converted into binary code that the CPU can understand. A
compiler
will directly translate the program code into binary (or executable) code, which can be later
executed. For example, in Windows executable files have the extension
.exe
. Conversely,
an
interpreter
interprets the program. It translates every line of code into executable code,
which is then executed. A file that contains the executable code is not created. An interpreter
is usually slower than a compiler because each line of code needs to be translated into
executable code before it can be executed.
Java takes an approach that uses both a compiler and interpreter. Java code is compiled
into Java binary code, which is different than the binary code that the CPU can understand.
This binary code can be later executed by a
Java Virtual Machine (JVM)
interpreter. This
