convert the decimal number 19/4 into binary system
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).
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To convert the decimal number 19/4 into the binary system, you need to follow these steps:
Step 1: Convert the whole number part
Divide the numerator (19) by the denominator (4) to get the quotient and the remainder:
19 ÷ 4 = 4 with a remainder of 3.
The quotient (4) will be the whole number part of the binary representation.
Step 2: Convert the fractional part
To convert the fractional part, you need to multiply it by 2 and keep track of each bit in binary representation.
Take the remainder from the previous step (3) and multiply it by 2:
3 × 2 = 6.
The whole number part of the result (6) becomes the first bit after the decimal point.
Now, take the decimal part of the result (0) and multiply it by 2:
0 × 2 = 0.
The decimal part of the result (0) becomes the second bit after the decimal point.
Continue this process until you either reach the desired level of precision or you get a repeating pattern.
Step 3: Combine the whole and fractional parts
Combine the whole number part from Step 1 (4) with the fractional part from Step 2 (0.0) to get the final binary representation.
Therefore, the decimal number 19/4 in binary is 100.0.