4) CONVERSIONS :
i) (5432) 8 = (?)16
ii)
(19CF) 16 = = (?)
iii) (12345) 10 = (?)
iv) (A01E) 16 = (?)10
v) (11010010101) 2 = (?)10
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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 :
- Divide the number by 2
- Take the quotient to the next iteration
- take the remainder for the binary digits
- Repeat the steps until the quotient is 0
Similarly do the other conversions.
iv) (A01E)₁₆ = (40990)₁₀
v) (11010010101)₂ = (1685)₁₀
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