Convert 224 to binary.
Understand the Problem
The question is asking to convert the decimal number 224 into binary format. This involves dividing the number by 2 and recording the remainders to build the binary representation.
Answer
11100000
Answer for screen readers
The final answer is 11100000
Steps to Solve
- Divide the number by 2 and record the quotient and remainder
Take 224 and divide by 2. Record the remainder, which will be either 0 or 1. Repeat this with the quotient until the quotient is 0.
$$\begin{align*} 224 \div 2 &= 112 , \text{quotient} , 0 , \text{remainder} \ 112 \div 2 &= 56 , \text{quotient} , 0 , \text{remainder} \ 56 \div 2 &= 28 , \text{quotient} , 0 , \text{remainder} \ 28 \div 2 &= 14 , \text{quotient} , 0 , \text{remainder} \ 14 \div 2 &= 7 , \text{quotient} , 0 , \text{remainder} \ 7 \div 2 &= 3 , \text{quotient} , 1 , \text{remainder} \ 3 \div 2 &= 1 , \text{quotient} , 1 , \text{remainder} \ 1 \div 2 &= 0 , \text{quotient} , 1 , \text{remainder} \end{align*}$$
- Write down the remainders in reverse order
The binary representation is formed by the remainders read from bottom to top.
Reading the remainders from the bottom up, we get: 11100000
The final answer is 11100000
More Information
Binary numbers are essential in digital electronics and computer systems because they represent on and off states.
Tips
A common mistake is not recording the remainders correctly or reading the remainders in the wrong order. Always ensure you write down the remainders as you go and then read them from the bottom up.
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