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Question 1
Convert the following numbers to base 2, base 8, base 10 and base 16.
(i)6910
(ii)6768
(iii)2F16
(iv)10011012

Answers:
i.Base 2 Base8 Base16
2 69 8 69 16 69
2 34 -1 8 8-5 16 4-5
2 17 -0 8 1-0
2 8 -1
2 4 -0
2 2 -0
2 1 -1

ii. Base2 Base10 Base16

2 446 (6×82 ) 16 676
2 223-0 (7×81) 16 42-4
2 111-1 +(6×80) 16 2-10
2 55-1 = =
2 27-1
2 13-1
2 6-1
2 3-0
2 1-1
=

iii.
Base2 Base8 Base10

2 215 8 215 (2×162)
2 107-1 8 26-7 (1×161)
2 53-1 8 3-2 (5×160)
2 26-1 = =
2 13-0
2 6-1
2 3-0
2 1-1

=

iv.Base16 Base8 Base10

16 77 8 77 (1×26)
16 4-13 8 9-5 (0x25)
8 1-1 (0x24)
(1×23)
(1×22)
(0x21)
(1×20)
= = =

Question 3

Calculate the following matrix equations.
(i)-14 -3 -5
5 4 7

(ii) 6 -2 -10 9 + 2 5 -2 3
6 0 4 -1 0 4

Answers:
i.=
ii.+=

Question 4
Factor the following equations and find the values of x.
(i)2×2 – 11x + 15
(ii)x2 – 4x – 45
(iii)-15×2 + 16x – 4
Answers:

i.(2x-5)(x-3) x=3or x=-3
ii.(x+5)(x-9)x=5 or x=9
iii.(-5x+2)(3x-2)x=2 or x=-2

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