What is the largest negative decimal value that can be represented by a two-byte number

 What is the largest negative decimal value that can be represented by a two-byte number?

The correct answer and explanation is :

The largest negative decimal value that can be represented by a two-byte number is -32,768.

Explanation:

A two-byte number consists of 16 bits. In computing, these bits can represent a range of numbers depending on whether the number is signed or unsigned. A signed two-byte number uses one bit (the leftmost or most significant bit) to represent the sign of the number, with 0 indicating positive and 1 indicating negative numbers. This leaves the remaining 15 bits to represent the magnitude of the number.

For a signed two-byte (16-bit) number:

• One bit is used for the sign.
• The remaining 15 bits are used to represent the magnitude of the number.

In binary representation, this means that the range of values is determined by two factors:

1. The number of bits available for the magnitude (15 bits in this case).
2. The sign bit, which flips the magnitude to represent negative numbers.

Range of Signed Two-Byte Numbers:

• Maximum Positive Value: The largest positive value occurs when all the bits are set to 0 except the sign bit. This results in the number represented by 15 bits of 1, which equals 32,767 in decimal (binary: 0111111111111111).
• Maximum Negative Value: The largest negative value occurs when the sign bit is set to 1 and all the remaining bits are set to 0. This is represented by the binary value 1000000000000000, which equals -32,768 in decimal.

Thus, the range of signed two-byte numbers is from -32,768 to 32,767.

Why -32,768?

The number -32,768 represents the smallest (most negative) value because in the two’s complement notation (which is commonly used to represent signed integers in binary systems), the most negative number is achieved by setting the sign bit to 1 and all the other bits to 0. This gives the number -32,768 as the largest negative decimal value that can be represented with a two-byte signed integer.

This is the largest negative value because, in two’s complement, negative numbers are represented by the complement of the magnitude, and -32,768 is the lowest point before wrapping around to positive values.