What is the binary representation of decimal 7?

What is the binary representation of decimal 7?

• A. 101
• B. 110
• C. 111
• D. 1000

Answer: (C)

To convert a decimal number like 7 into binary, you need to represent it using powers of 2. The binary system is base-2, meaning every digit represents an increasing power of 2, starting from the rightmost digit. For the number 7, you can break it down as follows: - The closest power of 2 less than or equal to 7 is 4, which is \(2^2\). - The next power of 2 is 2, which is \(2^1\). - Finally, the least power of 2 is 1, which is \(2^0\). Thus, you can express 7 as: - \(4 + 2 + 1\) = \(2^2 + 2^1 + 2^0\). In binary, each of these powers corresponds to a '1' in their respective position: - \(2^2\) (4) contributes a '1' in the third position from the right. - \(2^1\) (2) contributes a '1' in the second position. - \(2^0\) (1) contributes a '1' in the first position. So, the binary

To convert a decimal number like 7 into binary, you need to represent it using powers of 2. The binary system is base-2, meaning every digit represents an increasing power of 2, starting from the rightmost digit.

For the number 7, you can break it down as follows:

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

• The next power of 2 is 2, which is (2^1).

• Finally, the least power of 2 is 1, which is (2^0).

Thus, you can express 7 as:

• (4 + 2 + 1) = (2^2 + 2^1 + 2^0).

In binary, each of these powers corresponds to a '1' in their respective position:

• (2^2) (4) contributes a '1' in the third position from the right.

• (2^1) (2) contributes a '1' in the second position.

• (2^0) (1) contributes a '1' in the first position.

So, the binary