What is the binary equivalent of the decimal number 47?

What is the binary equivalent of the decimal number 47?

• A. 00101101
• B. 00101111
• C. 00111011
• D. 00100011

Answer: (B)

To convert the decimal number 47 into binary, it's essential to understand how the binary system represents values based on powers of 2. The binary system is base 2, and each digit (bit) can only be a 0 or a 1. The value of the decimal number 47 can be broken down as follows: - The highest power of 2 less than or equal to 47 is 32 (which is \(2^5\)). - Subtracting 32 from 47 gives us 15. - The next highest power of 2 less than or equal to 15 is 8 (which is \(2^3\)). - Subtracting 8 from 15 gives us 7. - The next highest power of 2 less than or equal to 7 is 4 (which is \(2^2\)). - Subtracting 4 from 7 gives us 3. - The next highest power of 2 less than or equal to 3 is 2 (which is \(2^1\)). - Subtracting 2 from 3 gives us 1, where 1 is \(2^0\). By combining these powers of 2

To convert the decimal number 47 into binary, it's essential to understand how the binary system represents values based on powers of 2. The binary system is base 2, and each digit (bit) can only be a 0 or a 1.

The value of the decimal number 47 can be broken down as follows:

• The highest power of 2 less than or equal to 47 is 32 (which is (2^5)).

• Subtracting 32 from 47 gives us 15.

• The next highest power of 2 less than or equal to 15 is 8 (which is (2^3)).

• Subtracting 8 from 15 gives us 7.

• The next highest power of 2 less than or equal to 7 is 4 (which is (2^2)).

• Subtracting 4 from 7 gives us 3.

• The next highest power of 2 less than or equal to 3 is 2 (which is (2^1)).

• Subtracting 2 from 3 gives us 1, where 1 is (2^0).

By combining these powers of 2