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Task Answer the following Questions Question 1 a) Determine the value of base x if (152)x = (6A)16 Please show all steps. b) Convert the followings: (Please show all steps) i) 0xBED into 3-base representation ii) 3217 into 2-base (binary) representation iii) 1235 into octal representation iv) 21.218 into decimal representation c) Given a (very) tiny computer that has a word size of 3 bits, what are the lowest value (negative number) and the highest value (positive number) that this computer can ...

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Solutions

a)     (152)x= (6A)16   

ð X2 + (5 * X1) + (2 * X0) = (6 * 161) + (10 * 160)

ð X2 + 5X + 2 = 106

ð X2 + 5X  - 104 = 0

ð X2 + 13X  - 8X – 104 = 0

ð X(X + 13) – 8(X + 13) = 0

ð (X - 8) (X + 13) = 0

ð X = 8 and X = -13

So, the value of X is 8

b)     Conversions

1)     BED16 to base 3

BED = (B * 162) + (E * 161) + (D * 160)

      = 2816 + 224 + 13

      =305310

(3053)10 = 

BED16 = (11012002)3

2)     3217 changing  into 2-base

3217  =  (3 * 72) + (2 * 71) + (1 * 70)

      = (162)10

(162)10 =

(162)10 = (10100010)2

3)     1235 converting into octal representation

(1235) = (2323)8

4)     21.218 converting into decimal representation

21.218 = (2 * 81) + (1 * 80). (2 * 8-1) + (1 * 7=8-2)

      = 17 + 0.25 + 0.015625

      = 17.265625

c)     i) In a computer of 3 word size, one’s Complement lowest number = 100

In a computer of 3 word size, one’s Complement lowest number of word size 3 bit = 011

ii) In a computer of 3 word size, two’s Complement lowest number of word size 3 bit = 101

In a computer of 3 word size,  two’s Complement lowest number of word size 3 bit = 011

iii) In a computer of 3 word size, signed Magnitude lowest number of word size 3 bit = 111

In a computer of 3 word size,  signed Magnitude lowest number of word size 3 bit = 011

OR

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