RECURSION - Java Programming: From Problem Analysis to Program Design - page 904

Test your program on the following data:
9098 and base 20
692 and base 2
753 and base 16
15. Binary to Decimal Conversion. The language of a computer, called
machine language, is a sequence of 0s and 1s. When you press the A key on
the keyboard, 01000001 is stored in the computer. Note that the collating
sequence of A in the Unicode character set is 65 . In fact, the binary
representation of A is 01000001 and the decimal representation of A is 65 .
The numbering system we use is called the decimal system, or base 10
system. The numbering system that the computer uses is called the binary
system, or base 2 system. This chapter described how to convert a decimal
number into an equivalent binary number. The purpose of this exercise is
to write a program to convert a number from base 2 to base 10.
To convert a number from base 2 to base 10, we first find the weight of
each bit in the binary number. The weight of each bit in the binary number
is assigned from right to left. The weight of the rightmost bit is 0. The
weight of the bit immediately to the left of the rightmost bit is 1, the weight
of the bit immediately to the left of it is 2, and so on. Consider the binary
number 1001101 . The weight of each bit is as follows:

weight 6 5 4 3 2 1 0

1 0 0 1 1 0 1

We use the weight of each bit to find the equivalent decimal number. For each
bit, we multiply the bit by 2 to the power of its weight and then add all of the
numbers. For the above binary number, the equivalent decimal number is:
1 2 6 þ 0 2 5 þ 0 2 4 þ 1 2 3 þ 1 2 2 þ 0 2 1 þ 1 2 0
¼ 64 þ 0 þ 0 þ 8 þ 4 þ 0 þ 1
¼ 77
To write a program that converts a binary number into the equivalent decimal
number, we note two things: (1) the weight of each bit in the binary number
must be known; and (2) the weight is assigned from right to left. Because we
do not know in advance how many bits are in the binary number, we must
process the bits from right to left. After processing a bit, we can add 1 to its
weight, giving the weight of the bit immediately to its left. Also, each bit must
be extracted from the binary number and multiplied by 2 to the power of its
weight. To extract a bit, you can use the mod operator. Write a method that
converts a binary number into an equivalent decimal number. Moreover,
write a program and test your method for the following values: 11000101 ,
10101010 , 11111111 , 10000000 ,and 1111100000 .