## Question 1 Convert the following numbers to base 2

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