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

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2. Multiplication / Division follow which operation?

a) XOR

b) NAND

c) AND

d) OR

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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

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4. How many numbers cannot be used in GF(p) in 2n where n=4?

a) 2

b) 5

c) 3

d) 1

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5. If f(x)=x^{3}+x^{2}+2 and g(x)=x^{2}-x+1, find: f(x) + g(x)

a) x^{3}+2x^{2}-x+3

b) x^{3}+x^{2}+3

c) x^{3}+x+1

d) x^{2}+2x+4

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6. If f(x)=x^{3}+x^{2}+2 and g(x)=x^{2}-x+1, find: f(x) – g(x)

a) x^{3}+x+4

b) x^{3}+x+1

c) x^{3}+x^{2}+3

d) x^{3}+3x+2

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7. If f(x)=x^{4}+x^{3}+2 and g(x)=x^{3}-x+6, find: f(x) + g(x)

a) 2x^{4}+2x^{3}+x+8

b) x^{4}+2x^{3}-x+8

c) x^{4}+x^{2}+x+8

d) x^{4}+x^{3}+8

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8. If f(x)=x^{4}+x^{2}-x+2 and g(x)=x^{2}-x+1, find: f(x) – g(x)

a) x^{4}+1

b) x^{2}+1

c) x^{2}+2x+6

d) x^{4}-1

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9. If f(x)=x^{3}+x^{2}+2 and g(x)=x^{2}-x+1, find the quotient of f(x) / g(x)

a) x+3

b) x^{2}+4

c) x

d) x+2

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10. If f(x)=x^{3}+x^{2}+2 and g(x)=x^{2}-x+1, find: f(x) x g(x)

a) x^{4}+x^{2}+2x+2

b) x^{5}+2x^{3}+2x+3

c) x^{5}+3x^{2}-2x+2

d) x^{4}+x^{2}+x+1

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11. Find the 8-bit word related to the polynomial x^{5} + x^{2} + x

a) 00010011

b) 01000110

c) 00100110

d) 11001010

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12. Find the 8-bit word related to the polynomial x^{6} + x^{5} + x^{2} + x +1

a) 00010011

b) 11000110

c) 00100110

d) 01100111