A method for representing signed integers in binary where the most significant bit indicates the sign is called:

A method for representing signed integers in binary where the most significant bit indicates the sign is called:

• A. Two's Complement Representation
• B. Sign-Magnitude Representation
• C. One's Complement Representation
• D. Gray Code

Answer: (A)

This question tests how a sign is carried in binary encoding. In sign-magnitude representation, the most significant bit serves as a sign flag: 0 means nonnegative and 1 means negative, while the remaining bits indicate the magnitude. So with n bits, the pattern splits into a sign bit and an (n−1)-bit magnitude. For example, with 4 bits, +3 is 0 011 and −3 is 1 011. There are two representations of zero: +0 (0 000) and −0 (1 000). This approach makes the sign explicit, but it comes with dual zeros and can complicate arithmetic. This contrasts with two's complement, where negatives are formed by inverting all bits and adding one, so there isn’t a separate sign bit and arithmetic operations remain uniform with a single zero. One's complement is similar but doesn’t add one, also yielding two zeros. Gray code is a different coding scheme used to minimize bit changes, not a standard signed-integer representation.

This question tests how a sign is carried in binary encoding. In sign-magnitude representation, the most significant bit serves as a sign flag: 0 means nonnegative and 1 means negative, while the remaining bits indicate the magnitude. So with n bits, the pattern splits into a sign bit and an (n−1)-bit magnitude.

For example, with 4 bits, +3 is 0 011 and −3 is 1 011. There are two representations of zero: +0 (0 000) and −0 (1 000). This approach makes the sign explicit, but it comes with dual zeros and can complicate arithmetic.

This contrasts with two's complement, where negatives are formed by inverting all bits and adding one, so there isn’t a separate sign bit and arithmetic operations remain uniform with a single zero. One's complement is similar but doesn’t add one, also yielding two zeros. Gray code is a different coding scheme used to minimize bit changes, not a standard signed-integer representation.