What is the binary representation of the decimal number 7?

To find the binary representation of the decimal number 7, we start by understanding how binary counting works. In binary, each digit represents a power of two, starting from the rightmost digit, which represents (2^0), the next one (2^1), then (2^2), and so on.

The decimal number 7 can be broken down into powers of two as follows:

• (2^2) (which equals 4) contributes to the sum.

• (2^1) (which equals 2) also contributes to the sum.

• (2^0) (which equals 1) contributes to the sum.

When we add these powers together, we get (4 + 2 + 1 = 7). In binary, we denote the presence of these powers with a '1' and their absence with a '0'. Therefore, in binary representation:

• (2^2) is included (1),

• (2^1) is included (1),

• (2^0) is included (1).

This gives us the binary number 111 for (2^2, 2^1,) and (2^0