Question

4) CONVERSIONS :
i) (5432) 8 = (?)16
ii)
(19CF) 16 = = (?)
iii) (12345) 10 = (?)
iv) (A01E) 16 = (?)10
v) (11010010101) 2 = (?)10​

Answer 1

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Answer 2

i) (5432)₈ = (B1A)₁₆

First write binary of 5432 : 101 100 011 010

Make groups of 4 starting from right to left

1011 0001 1010

Now write hexa-decimal value for the groups

1011 0001 1010 =  B 1 A

So, (5432)₈ = (B1A)₁₆

ii) (19CF)₁₆ = (1100111001111) ₂ = (14717)₈ = (6607)₁₀

To covert from hexa-decimal to binary, write the binary for each characters

1 = 0001

9 = 1001

C = 1100

F = 1111

1 9 C F = 0001 1001 1100 1111

So, (19CF)₁₆ = (1100111001111) ₂

iii) (12345)₁₀ = (11000000111001) ₂ = (30071)₈ = (3039)₁₆

Covert decimal to binary :

1. Divide the number by 2
2. Take the quotient to the next iteration
3. take the remainder for the binary digits
4. Repeat the steps until the quotient is 0

Similarly do the other conversions.

iv) (A01E)₁₆ = (40990)₁₀

v) (11010010101)₂ = (1685)₁₀