SELECTIONS - Introduction to Java Programming - page 89

line# output

day answer

35 0

44 1

47 1

53 1

56 3

62 0

71 0

80 1

83 19

85 Your birthday is 19!

This game is easy to program. You may wonder how the game was created. The mathematics
behind the game is actually quite simple. The numbers are not grouped together by accident—
the way they are placed in the five sets is deliberate. The starting numbers in the five sets are 1 ,
2 , 4 , 8 , and 16 , which correspond to 1 , 10 , 100 , 1000 , and 10000 in binary (binary numbers are
introduced in Appendix F, Number Systems). A binary number for decimal integers between 1
and 31 has at most five digits, as shown in Figure 3.2a. Let it be Thus,
as shown in Figure 3.2b. If a day's binary
number has a digit 1 in the number should appear in Set k . For example, number 19 is
binary 10011 , so it appears in Set1, Set2, and Set5. It is binary 1 + 10 + 10000 = 10011 or
decimal 1 + 2 + 16 = 19 . Number 31 is binary 11111 , so it appears in Set1, Set2, Set3, Set4,
and Set5. It is binary 1 + 10 + 100 + 1000 + 10000 = 11111 or decimal 1 + 2 + 4 +
8 + 16 = 31 .

mathematics behind the game

b 5 b 4 b 3 b 2 b 1 .

b 5 b 4 b 3 b 2 b 1 = b 5 0000 + b 4 000 + b 3 00 + b 2 0 + b 1 ,

b k ,

Decimal Binary

10000
1000
100
10

b 5

0 0 00

1 00001

b 4

00

0

2 00010

00011

10000
10
1

b 3

0 0

3
...
19

b 2

0

+ + 1

11111

b 1
b 5 b 4 b 3 b 2 b 1

+

10011

10011
19

...
31 11111 31

(a) (b)

F IGURE 3.2 (a) A number between 1 and 31 can be represented using a 5-digit binary
number. (b) A 5-digit binary number can be obtained by adding binary numbers 1 , 10 , 100 ,
1000 , or 10000 .

3.5 Two-Way if-else Statements
An if-else statement decides which statements to execute based on whether the
condition is true or false.

Key
Point

A one-way if statement takes an action if the specified condition is true . If the condition is
false , nothing is done. But what if you want to take alternative actions when the condition is
false ? You can use a two-way if-else statement. The actions that a two-way if-else
statement specifies differ based on whether the condition is true or false .