Mini Quiz 1 Structure

• Four questions
• Question 1: Convert binary number to decimal. Explain your answer
• Question 2: Convert decimal number to binary using BOTH methods explained in class. Write your answer as 1 BYTE number ( 1 BYTE = 8 BITS) Explain your answer.
• Question 3: Encoding short word (2-3 letters) into binary. Explain ONE letter in detail.
• Question 4: Decoding short binary sequence into sequence of characters (3-4 letters). Explain ONE BYTE in detail.
• Range of the numbers is: 0 - 255
• ASCII TABLE (will be provided).

Exampes

1. Convert binary number 1100 1101 to decimal
   Solution: add power of 2 that corresponds to the bits that are ON ( bits that are equal 1):
   128 + 64 + 8 + 4 + 1 = 205

   Final answer: 205 is decimal equivalent of binary number 1100 1101

2. Convert decimal 38 to binary:
   Solution Method 1:
   128 fits into 38? NO b7 = 0
   64 fits into 38? NO b6 = 0
   32 fits into 38? YES b5 = 1
   38 - 32 = 6
   Continue with 6:
   16 fits into 6? NO b4 = 0
   8 fits into 6? NO b3 = 0
   4 fits into 6 YES b2 = 1
   6 - 4 = 2
   Continue with 2:
   2 fits into 2? YES b1 = 1
   2-2 = 0
   Continue with 0:
   1 fits into 0? NO b0 = 0

   Final answer: Decimal number 38 in binary is 0010 0110

   Method 2 using Integer Division and Remainder:
   38 / 2 = 19 remainder 0 b0 = 0
   19 / 2 = 9 remainder 1 b1 = 1
   9 / 2 = 4 remainder 1 b2 = 1
   4 / 2 = 2 remainder 0 b3 = 0
   2 / 2 = 1 remainder 0 b4 = 0
   1 / 2 = 0 remainder 1 b5 = 1
   As soon as we got 0 the process is stopped and the rest of the bits are 0: b6 = 0, b7 =0

   Final Answer: Decimal number 38 in binary system is: 0010 0110

3. Convert binary number 0100 0100 to decimal
   Solution: add power of 2 that corresponds to the bits that are ON ( bits that are equal 1):
   64 + 4 = 68

   Final answer: 68 is decimal equivalent of binary number 0100 0100

4. Convert decimal 121 to binary:
   Solution Method 1:
   128 fits into 121? NO b7 = 0
   64 fits into 121? YES b6 = 1
   121 - 64 = 57
   Continue with 57
   32 fits into 57? YES b5 = 1
   57 - 32 = 25
   Continue with 25:
   16 fits into 25? YES b4 = 1
   25 - 16 = 9
   Continue with 9
   8 fits into 9? YES b3 = 1
   9 - 8 = 1
   Continue with 1
   4 fits into 1? NO b2 = 0
   2 fits into 1? NO b1 = 0
   1 fits into 1? YES b0 = 1

   Final answer: Decimal number 121 in binary is 0111 1001

   Method 2 using Integer Division and Remainder:
   121 / 2 = 60 remainder 1 b0 = 1
   60 / 2 = 30 remainder 0 b1 = 0
   30 / 2 = 15 remainder 0 b2 = 0
   15 / 2 = 7 remainder 1 b3 = 1
   7 / 2 = 3 remainder 1 b4 = 1
   3 / 2 = 1 remainder 1 b5 = 1
   1 / 2 = 0 remainder 1 b6 = 1
   As soon as we got 0 the process is stopped and the rest of the bits are 0:b7 =0

   Final Answer: Decimal number 121 in binary system is: 0111 1001

5. Convert Go! to binary
   Solution: Go! in ASCII is: 71 111 33
   71 to binary:
   71/2 = 35 b0 = 1
   35/2 = 17 b1 = 1
   17/2 = 8 b2 = 1
   8/2 = 4 b3 = 0
   4/2 = 2 b4 = 0
   2/2 = 1 b5 = 0
   1/2 = 0 b6 = 1
   71 in binary: 0100 0111
   111 in binary: 0110 1111
   33 in binary: 0010 0001

   Final answer: Go! in binary: 01000111 01101111 00100001

6. Decode: 01101101 01000101 00110010
   Solution: converting each BYTE to decimal
   0110 1101 adding powers of 2 that are ON: 64 + 32 + 8 + 4 + 1 = 109
   0100 0101 is 69
   0011 0010 is 50
   Original message in ASCII 109 69 50

   Final answer: decoded word: mE2

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   Programming with Python

   Online Resource

   Problem Solving in C and Python: Programming Exercises and Solutions, Part 1 By Yana Kortsarts, Yulia Kempner, Leonid Kugel, Adam Fischbach (editor), Zuny Jamatte (cover design/art creator), & Michal Kortsarts (cover design/art creator)

   Input and Formatted Output in Python:

   • For integers use: int(input("user prompt "))

   • For floats use: float(input("user prompt "))

   • For strings use: input("user prompt ") and when inputing the string you must enclose it in double or single quotes

   • For formatted output use function format.
     • For example, to print only 2 decimal digits of the number 1232.566777 use the following statement:

       print(format(1232.566777, '.2f'))

     • For example, to print only 4 decimal digits of the number 1232.566777 use the following statement:

       print(format(1232.566777, '.4f'))