1. “A very common field in this category is GF(2) with the set {1, 2} and two operations, addition and multiplication.”
a) True
b) False
Answer
Answer: b [Reason:] GF(2) is the set {0, 1} with two operations, addition and multiplication
2. Multiplication / Division follow which operation?
a) XOR
b) NAND
c) AND
d) OR
Answer
Answer: c [Reason:] Multiplication / Division is the same as the AND operations.
3.
0 1 2 3 4
0 4 3 2 1
0 1 2 3 4
– 1 3 2 4
What do the above numbers correspond to?
a) Both Additive Inverses
b) Both Multiplicative Inverses
c) Additive and Multiplicative Inverse respectively
d) Multiplicative and Additive Inverses respectively
Answer
Answer: b [Reason:] The top set of numbers correspond to Additive Inverses and the bottom set of numbers correspond to Multiplicative Inverse.
4. How many numbers cannot be used in GF(p) in 2n where n=4?
a) 2
b) 5
c) 3
d) 1
Answer
Answer: c [Reason:] If n=4, the largest prime less than 24 is 13. This means that we cannot use the integers 13, 14 and 15.
5. If f(x)=x3+x2+2 and g(x)=x2-x+1, find: f(x) + g(x)
a) x3+2x2-x+3
b) x3+x2+3
c) x3+x+1
d) x2+2x+4
Answer
Answer: a [Reason:] We get the solutions via basic polynomial addition.
6. If f(x)=x3+x2+2 and g(x)=x2-x+1, find: f(x) – g(x)
a) x3+x+4
b) x3+x+1
c) x3+x2+3
d) x3+3x+2
Answer
Answer: b [Reason:] We get the solutions via basic polynomial subtraction.
7. If f(x)=x4+x3+2 and g(x)=x3-x+6, find: f(x) + g(x)
a) 2x4+2x3+x+8
b) x4+2x3-x+8
c) x4+x2+x+8
d) x4+x3+8
Answer
Answer: b [Reason:] Perform polynomial addition.
8. If f(x)=x4+x2-x+2 and g(x)=x2-x+1, find: f(x) – g(x)
a) x4+1
b) x2+1
c) x2+2x+6
d) x4-1
Answer
Answer: a [Reason:] Perform polynomial subtraction.
9. If f(x)=x3+x2+2 and g(x)=x2-x+1, find the quotient of f(x) / g(x)
a) x+3
b) x2+4
c) x
d) x+2
Answer
Answer: d [Reason:]We get the solution via basic polynomial division.
10. If f(x)=x3+x2+2 and g(x)=x2-x+1, find: f(x) x g(x)
a) x4+x2+2x+2
b) x5+2x3+2x+3
c) x5+3x2-2x+2
d) x4+x2+x+1
Answer
Answer: c [Reason:] We get the solution via basic polynomial multiplication.
11. Find the 8-bit word related to the polynomial x5 + x2 + x
a) 00010011
b) 01000110
c) 00100110
d) 11001010
Answer
Answer: c [Reason:] The respective 8-bit word is 00100110.
12. Find the 8-bit word related to the polynomial x6 + x5 + x2 + x +1
a) 00010011
b) 11000110
c) 00100110
d) 01100111
Answer
Answer: d [Reason:] The respective 8-bit word is 01100111.
