Lab 7: Information representation and binary numbers

In this lab you will practice with information representation and binary numbers. Feel free to work in pairs.

Exercise 1: Some Questions

Answer the following questions:

• If you want to represent 57 different things by assigning a unique bit pattern to each of the 57 different things, how many bits would be required?


• Convert this bit string represented in ASCII code (01001010011000010111011001100001) into keys in a typical keyboard.


• What happens when you type in 1247 as an integer input on your keyboard for your program that reads in an integer number? Describe an algorithm verbally to your classmate (or to yourself).

Exercise 2: Binary Number Addition

Add the binary numbers given below:

       1010101010            1010111011
     +  101011111          + 1101110110
    -------------         -------------

Exercise 3: Binary Number Subtraction

Do the subtractions given below:

       1010101010            1010101010
     -  101011111          -  110111011
    -------------         -------------

Exercise 4: Converting from Decimal to Binary

Convert the following numbers from decimal to binary:

   15, 70, and 111.

Exercise 5: Converting from Binary to Decimal

Convert the following numbers from binary to decimal:

   1001, 10011, and 110110.

Exercise 6: Evaluating Boolean Expressions

Suppose we have a fragment of Java code as follows:

  boolean a = true;
  boolean b = false;
  boolean c = true;
  boolean b = a || (b && c);
  boolean d = a && (b || c) || (!a);

What is the resulting value of b and d if we execute these lines in order? Hint: the order of operator precedence is !, &&, and || in that order ! being the highest. We also evaluate from left to right.