To convert the decimal number 524 into its binary equivalent, follow these steps:
1. Understand the binary system: The binary numeral system represents values using two symbols: 0 and 1. Each digit in a binary number represents a power of 2.
2. Find the highest power of 2 less than or equal to 524:
- [tex]\(2^9 = 512\)[/tex]
3. Subtract 512 from 524:
- [tex]\(524 - 512 = 12\)[/tex]
4. Find the highest power of 2 less than or equal to 12:
- [tex]\(2^3 = 8\)[/tex]
5. Subtract 8 from 12:
- [tex]\(12 - 8 = 4\)[/tex]
6. Find the highest power of 2 less than or equal to 4:
- [tex]\(2^2 = 4\)[/tex]
7. Subtract 4 from 4:
- [tex]\(4 - 4 = 0\)[/tex]
8. Write down the binary representation:
- For 524, the powers of 2 used are [tex]\(2^9\)[/tex], [tex]\(2^3\)[/tex], and [tex]\(2^2\)[/tex]. These correspond to positions 9, 3, and 2 in the binary number.
9. Construct the binary number:
- The binary place values from right to left are [tex]\(2^0, 2^1, 2^2, 2^3, \ldots, 2^9\)[/tex].
- Place '1' in the positions for [tex]\(2^9, 2^3,\)[/tex] and [tex]\(2^2\)[/tex] and '0' in all other positions.
So the binary representation of 524 is:
[tex]\[
1000001100_2
\][/tex]
Therefore, the decimal number 524 converted to binary is:
[tex]\[ 524_{10} = 1000001100_2 \][/tex]
