Question

Convert $(23.8125)_{10}$ to its binary equivalent.

Answer 1

Given, Decimal Equivalent is (23.8125)₁₀.

How to convert Decimal Equivalent to binary:

(i) The number which is to be converted is multiplied by base of binary(2)

(ii) This process is continued until the fractional part becomes 0.

Step by Step Explanation:

(i) 0.8125 * 2 = 1.625

(ii) 0.625 * 2 = 1.25

(iii) 0.25 * 2 = 0.5

(iv) 0.5 * 2 = 1.0

(v)  0 * 0   ------- > Here, the fractional part is 0.  So, we have to stop here.

Integer parts:

From the above calculations, the integer parts are:

(i) 1

(ii) 1

(iii) 0

(iv) 1

Now, Arrange the integers from the most significant bit to least Significant bit.

So, the binary Equivalent of 0.8125 is (1101)₂.

So,the given Equivalent can be written as: (23.1101).

Now,

As, we know that 23 is also an integer, therefore it should be converted.

Number                   Quotient                  Remainder

23/2                           11                               1

11/2                             5                               1

5/2                              2                               1

2/2                              1                                0

1/2                               0                                1.

Thus, Binary Equivalent of 23 is (10111)₂.

Therefore, Binary Equivalent of (23.8125)₁₀ = (10111.1101)₂.

<!Hope it helps!>  

Answer 2

Answer:

10111.1101=23.8125

Explanation:

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