What is the binary equivalent of the decimal number 232?
Understand the Problem
The question is asking for the conversion of the decimal number 232 into its binary equivalent. To solve this, we typically divide the number by 2 and keep track of the remainders until we reach zero, and then read the remainders in reverse order.
Answer
$11101000_2$
Answer for screen readers
The binary equivalent of the decimal number 232 is $11101000_2$.
Steps to Solve
- Divide by 2 and Record the Remainder
Start by dividing the decimal number, 232, by 2. Keep track of the quotient and the remainder.
For example: $$ 232 \div 2 = 116 \quad \text{with a remainder of } 0 $$
- Repeat the Division Process
Continue dividing the quotient by 2, again recording the quotient and the remainder.
$$ 116 \div 2 = 58 \quad \text{with a remainder of } 0 $$
$$ 58 \div 2 = 29 \quad \text{with a remainder of } 0 $$
$$ 29 \div 2 = 14 \quad \text{with a remainder of } 1 $$
$$ 14 \div 2 = 7 \quad \text{with a remainder of } 0 $$
$$ 7 \div 2 = 3 \quad \text{with a remainder of } 1 $$
$$ 3 \div 2 = 1 \quad \text{with a remainder of } 1 $$
$$ 1 \div 2 = 0 \quad \text{with a remainder of } 1 $$
- Collect the Remainders
Now, gather all the remainders from the divisions. Starting from the last division to the first, the remainders are read in reverse order:
$$ 1, 1, 1, 0, 1, 0, 0, 0 $$
- Construct the Binary Equivalent
By reading the remainders in reverse order, we get the binary representation of the decimal number 232:
$$ 232_{10} = 11101000_2 $$
The binary equivalent of the decimal number 232 is $11101000_2$.
More Information
The binary numeral system is a base-2 system that uses only two digits, 0 and 1. It is widely used in computing and digital electronics because it aligns well with the binary logic of electrical circuits, where two states (on and off) are represented by these digits.
Tips
- Forgetting to record the remainders correctly during each division step can lead to an incorrect binary number.
- Reading the collected remainders in the wrong order (they should be read from last to first) can also lead to mistakes.
