convert the decimal number 19/4 into binary system

Answer 1

To convert the decimal number 19/4 into binary, we can use the following steps:

1. Convert the numerator and denominator of the fraction 19/4 into binary form.

19 in binary is 10011

4 in binary is 100

2. Divide the numerator by the denominator using binary division.

10011 / 100
= 1.0011

3. Separate the whole number and the fractional part.

Whole number: 1
Fractional part: 0.0011

4. Multiply the fractional part by 2 and repeat step 3.

0.0011 x 2 = 0.0110

Whole number: 0
Fractional part: 0.0110

5. Multiply the new fractional part by 2 and repeat step 3.

0.0110 x 2 = 0.1100

Whole number: 0
Fractional part: 0.1100

6. Multiply the new fractional part by 2 and repeat step 3.

0.1100 x 2 = 1.1000

Whole number: 1
Fractional part: 0.1000

7. Since the fractional part has repeated, we can stop here and write the binary representation as:

19/4 in binary is 100.01(1)

Therefore, the binary representation of the decimal number 19/4 is 100.01(1).

Answer 2

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