200 to binary
Understand the Problem
The question is asking us to convert the decimal number 200 into its binary equivalent. We will apply the process of dividing the number by 2 and keeping track of the remainders to find the binary representation.
Answer
11001000
Answer for screen readers
The final answer is 11001000
Steps to Solve
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Divide the number by 2 and record the remainder
Divide 200 by 2 and keep track of the quotient and remainder. Repeat this process with the quotient until you reach 0.
$$ 200 \div 2 = 100 \text{ remainder } 0 $$ $$ 100 \div 2 = 50 \text{ remainder } 0 $$ $$ 50 \div 2 = 25 \text{ remainder } 0 $$ $$ 25 \div 2 = 12 \text{ remainder } 1 $$ $$ 12 \div 2 = 6 \text{ remainder } 0 $$ $$ 6 \div 2 = 3 \text{ remainder } 0 $$ $$ 3 \div 2 = 1 \text{ remainder } 1 $$ $$ 1 \div 2 = 0 \text{ remainder } 1 $$
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Write the remainders in reverse order
Reading the remainders from bottom to top gives the binary representation of the number.
$$ 11001000 $$
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Combine the remainders to form the binary number
The final step is to combine the remainders we obtained in reverse order to form the binary number.
The final answer is 11001000
More Information
This method of converting decimal to binary is known as repeated division by 2. It is a straightforward and effective way to manually convert numbers between these bases.
Tips
A common mistake is forgetting to read the remainders in reverse order. Always start from the bottom remainder (last remainder obtained) and read upwards to get the correct binary number.
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