Express the following hexadecimal numbers into equivalent decimal numbers. (i) 4A2 (ii) 9E1A (iii) 6BD (iv) 6C.34
Question
Express the following hexadecimal numbers into equivalent decimal numbers.
(i) 4A2
(ii) 9E1A
(iii) 6BD
(iv) 6C.34
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Answer
To convert hexadecimal numbers to their equivalent decimal values, we can use the method of positional values. Here are the conversions:
(i) 4A2
List the hexadecimal digits and their decimal equivalents:
(4) -> (4)
(A) -> (10)
(2) -> (2)
Multiply each digit with $16^{\text{position}}$, where position starts from 0 on the right:
$$ 4 \times 16^2 + 10 \times 16^1 + 2 \times 16^0 = 4 \times 256 + 10 \times 16 + 2 \times 1 = 1024 + 160 + 2 = 1186 $$
So, $ (4A2)_{16} = (1186)_{10} $
(ii) 9E1A
List the hexadecimal digits and their decimal equivalents:
(9) -> (9)
(E) -> (14)
(1) -> (1)
(A) -> (10)
Multiply each digit with $16^{\text{position}}$, where position starts from 0 on the right:
$$ 9 \times 16^3 + 14 \times 16^2 + 1 \times 16^1 + 10 \times 16^0 = 9 \times 4096 + 14 \times 256 + 1 \times 16 + 10 \times 1 = 36864 + 3584 + 16 + 10 = 40474 $$
So, $ (9E1A)_{16} = (40474)_{10} $
(iii) 6BD
List the hexadecimal digits and their decimal equivalents:
(6) -> (6)
(B) -> (11)
(D) -> (13)
Multiply each digit with $16^{\text{position}}$, where position starts from 0 on the right:
$$ 6 \times 16^2 + 11 \times 16^1 + 13 \times 16^0 = 6 \times 256 + 11 \times 16 + 13 \times 1 = 1536 + 176 + 13 = 1725 $$
So, $ (6BD)_{16} = (1725)_{10} $
(iv) 6C.34
List the hexadecimal digits and their decimal equivalents:
(6) -> (6)
(C) -> (12)
(.3) -> $3 \times 16^{-1} = 3 \times \frac{1}{16} = \frac{3}{16}$
(.4) -> $4 \times 16^{-2} = 4 \times \frac{1}{256} = \frac{4}{256}$
Convert each part separately:
$$ 6 \times 16^1 + 12 \times 16^0 + 3 \times 16^{-1} + 4 \times 16^{-2} = 6 \times 16 + 12 + 0.1875 + 0.015625 = 96 + 12 + 0.1875 + 0.015625 = 108.203125 $$
So, $$ (6C.34){16} = (108.203125){10} $$
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