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).
convert the decimal number 19/4 into binary system
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