28 to binary
Understand the Problem
The question is asking how to convert the decimal number 28 into its binary representation. This involves expressing the number in base-2 format, which utilizes only the digits 0 and 1.
Answer
11100
Answer for screen readers
The final answer is 11100
Steps to Solve
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Divide the number by 2 and record the remainder
Start by dividing the number 28 by 2 and write down the quotient and remainder. The remainder will be either 0 or 1, which are the binary digits.
$$ 28 \div 2 = 14 , \text{remainder} , 0 $$
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Repeat the division for the quotient
Take the quotient (14) from the previous division and divide it by 2. Record the quotient and the remainder.
$$ 14 \div 2 = 7 , \text{remainder} , 0 $$
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Continue the process
Continue this process until the quotient is 0:
$$ 7 \div 2 = 3 , \text{remainder} , 1 $$ $$ 3 \div 2 = 1 , \text{remainder} , 1 $$ $$ 1 \div 2 = 0 , \text{remainder} , 1 $$
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Write the remainders in reverse order
The binary representation is obtained by writing the remainders from bottom to top (i.e., in reverse order of how they were calculated).
So, the binary representation of 28 is:
$$ 11100 $$
The final answer is 11100
More Information
The binary system is key in computer science where data is represented using binary digits (bits). Each bit has either a value of 0 or 1, which perfectly suits the electronic states of digital circuits (off and on).
Tips
Common mistakes include not reversing the remainder sequence or errors in the division and remainder steps. Always double-check your division and record the remainders correctly.
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