Convert the following numbers. ( show all steps; no marks will be awarded if no steps are shown) [1.5 x 4 = 6 marks]
i) 0xad9 into 3-base representation
ii) 4518 into 2-base (binary) representation
iii) 123.35 into octal representation (up to 3 octal points)
iv) 14.358 into decimal representation

i. 10210212

ii. 100 101 001 in BASE 2

iii. 46.4631

iv. 12.453125

Explanation:

i. Converting to base 10 we get

=  10 x 162 + 13 x 161 + 9 x 160 = 2777

Converting to base 10 we get  =

2777/3 = 925 with remainder 2

925/3 = 308 with remainder 1

308/3 = 102 with remainder 2

102/3 = 34 with remainder 0

34/3 = 11 with remainder 1

11/3 = 3 with remainder 2

3/3 = 1 with remainder 0

1/3 = 0 with remainder 1

Hence the Answer is 10210212

ii. = Octal is taken in pair of 3 bits , Writing binary of each number in 3 bits we get  = 100 101 001 in BASE 2

iii. = 1 x 52 + 2 x 51 + 3 x 50 + 3 x 5-1   = 38.6 in decimal

Converting to Octal we get

38 /8 = 4 with remainder 6

4 /8 = 0 with remainder 4

.6 x 8 =  4.8

.8 x 8 = 6.4

46.4631

iv. = 1x 81 + 4 x 80 + 3 x 8-1 + 5 x 8-2   = 12.453125

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