What is the binary equivalent of decimal 7?

To understand why the binary equivalent of the decimal number 7 is 111, it's essential to know how binary numbering works. In binary, each digit represents a power of 2, starting from the rightmost digit, which is (2^0), the next (2^1), followed by (2^2), and so on.

When converting the decimal number 7 into binary, we can break down how 7 can be represented using these powers of 2:

• (2^2) is 4, which is the largest power of 2 less than 7. If we use that, we have 4, leaving us with (7 - 4 = 3).

• (2^1) is 2, which can also be used. Subtracting 2 from 3 gives us (3 - 2 = 1).

• Finally, (2^0) is 1, which can be used, resulting in (1 - 1 = 0).

Now we have used (2^2), (2^1), and (2^0) to represent 7, which corresponds to a '1' in each