A negative decimal number can be represented in 16-bit binary format using the two’s complement method.

In computer science, negative numbers are commonly represented using the two’s complement technique. This approach is preferred due to its simplicity in arithmetic operations and its efficient alignment with binary number systems. To convert a negative decimal number into its 16-bit binary representation, one should first convert the absolute value of the number into binary, then invert all the bits (changing $1$s to $0$s and $0$s to $1$s), and finally add $1$ to the inverted result.

For instance, let’s consider the negative number $-18$. The binary representation of its absolute value, $18$, in 16 bits is:

To find the two’s complement, we first invert the bits:

Next, we add $1$ to this result:

Thus, the binary representation of $-18$ in 16-bit format is:

One of the main advantages of the two’s complement method is that it simplifies arithmetic operations. When you add a positive number and its negative equivalent in two’s complement form, the result will always be zero. This occurs because any carry from the highest bit, known as the sign bit, is discarded in fixed-width binary numbers, leading to a phenomenon referred to as “wrap around.”

It is important to note that in a two’s complement representation, the leftmost bit serves as the sign bit. If the sign bit is $0$, the number is positive; if it is $1$, the number is negative. This characteristic allows for quick identification of a number’s sign.

To summarize, to represent a negative decimal number in 16-bit binary, you can employ the two’s complement method: first convert the number to binary, then invert the bits, and finally add $1$. This method not only indicates the sign of the number (with $0$ for positive and $1$ for negative) but also facilitates arithmetic operations, making it easier to handle negative numbers in binary form.