Homework 1

• Represent the following quantities in 8 bit sign magnitude, BCD, and 8 bit twos compliment.
  • 134
  • 65
  • -24
• Give the addition table for base 3.
• Express the following in binary.
  • .6
  • .1875
• Complete the following table:

  Binary	Octal	Hexadecimal
  101101012
  	4728
  		A4716

• Give an algorithm for adding two numbers in each of the following systems.
  • BCD
  • Sign Magnitude
  • Stick Numbers
  • Twos compliment
• Compare your algorithms, which is more efficient in terms of
  • Storage
  • Ease of algorithm
• Encode "O Captain! My Captain!" in ascii
  • Give the binary representation
  • Give the hex representation.
• Create a huffman code for the following alphabet. When constructing your tree, always put the subtree with the smallest probability on the left hand side, and assign a 0 to all left hand branches.

  • Letter	Frequency
    A	0.07
    B	0.3
    C	0.15
    D	0.05
    E	0.25
    F	0.08
    G	0.09
    H	0.01

  • Encode the message ACFDGGHE
  • On average, what is the cost of encoding a 20 bit message in your code?
  • How many bits would a fixed length encoding for this alphabet require?
  • Is your code efficient?