AP Computer Science Java Programming - Binary and Hexadecimal

Binary and Hexadecimal Numbers

• People are used to base 10 numbers, this is totally different. Read from right to left to do the math.
  Ex. 256
  
• Binary is similar, but base 2, using only 0 and 1.
  Ex. 100110
  
• Hexadecimal is similar, but base 16, using 0-9 and A-F (10-15). Notice there are 16 numbers and letters total.
  Ex. 14D2
  

AP Sample Problems

Example 1

Suppose that base-2 (binary) numbers and base-16 (hex)
numbers can be denoted with subscript, as shown below:
2Ahex = 101010binary
Which is equal to 3Dhex?
(a) 111101
(b) 101111
(c) 10011

• Check all three with the math that I showed you from before and see which one is equivalent to 3D hex, or 61 in our regular numbering system.
  Answer: (a) 111101 = 1 + 4 + 8 + 16 + 32

Example 2

An example of a hex color is (238, 9, 63) --> ##EE093F
Which of the following would be (14, 20, 255)?

• Notice that the second number 9 is still 9 in the color code. The other two numbers are in hex, so convert 14 and 255 to hex, they are E and FF.
  Answer: ##0E20FF

Example 3

Consider the code segment:

int x = 10, y=0;
while (x > 5) {
y = 3;
while (y < x) {
y *= 2;
if (y % x == 1) {
y += x;
}
}
x -= 3;
}
System.out.println(x + “ “ + y);

• This code will run the outside while loop three times, changing the x and y values several times. You must read it line by line, as the computer would, until it is over.
  Answer: 4 12

Classwork/Homework:

Write a program that takes a binary number from the user,
entered only zeros and ones, that converts it to base 10 (our
regular number system). Only 4 digit numbers, like 1010 or 1110
or 0001. (Using mod operator is probably the best way).

Now, here are some outputs of my program:

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