Discrete Mathematics
Hans Georg Schaathun
4th January 2016

Exercises Week 11
Advanced Encryption Standard

Wednesday 28 October 2015

Please watch the videos once before class. It may be helpful to peek at the exercises between the videos. You should not worry if you do not understand them after the first run. We will discuss the exercises in class, and if that does help you start to understand, then you are allowed to worry.

1.1 Matrix calculations over finite sets

Exercise 1.1 Write the following numbers in Hexadecimal:

  1. 1024
    Decimal 1024 Hexadecimal 400
  2. 129
    Decimal 129 Hexadecimal 81
  3. 721

Exercise 1.2 Write the following numbers in Octal:

  1. 1024
  2. 129
    Decimal 129 Octal 201

Exercise 1.3 Write the following hexadecimal numbers in decimal:

  1. FF
    Hexadecimal FF Decimal 255
  2. 17A
  3. 111
    Hexadecimal 111 Decimal 273

Exercise 1.4 Rewrite hexadecimal A9 in binary.

Hexadecimal A9 Binary 10101001

Exercise 1.5 Write 0155 (octal) in decimal.

Exercise 1.6 Take the word ‘Try’, find the ASCII number for each letter, write it in binary form, and encode it using the parity check code.

  1. Translating to ASCII, we get 54, 72, 79 in Hexadecimal.
  2. In binary, this becomes (1010100),(1110010),(1111001)
  3. Encoding, with a parity check bit, we get (11010100),(01110010),(11111001)

1.2 Theory of finite fields

Exercise 1.7 Calculate the following over 2:

[101] + [110] =  (1) 11 1 0 0 1 + 10 0 1 0 1 =  (2)

Exercise 1.8 Calculate the following over 2:

[101] 11 1 0 0 1 =  (3) 100 0 0 1 111 0 1 0 0 01 =  (4)

Exercise 1.9 Calculate the following over 3:

  1. [121] + [210] =
    [121] + [210] = [1 + 2,2 + 1,1 + 0] = [0,0,1]

  2. [201] 11 2 0 0 1 =  (5)
  3. [121] [210] =

    [121] [210]T = 1 2 + 2 1 + 1 0 = 4
  4. 120 0 2 1 122 0 1 0 1 01 =  (6)
    120 0 2 1 122 0 1 0 1 01 = 112 1 2 1  (7)


Hans Georg Schaathun / hasc@hials.no