Digital arithmetic systems: what must be indicated for numbers? In digital electronics and computer arithmetic, any system that performs addition, subtraction, multiplication, or division must represent numbers unambiguously. Which pair of attributes must always be explicitly indicated for the represented numbers so that arithmetic operations are well-defined?

Introduction / Context:
Digital systems execute arithmetic on binary-encoded data. For any computation to be meaningful, the representation must clearly convey whether the value is positive or negative and how large it is. This question checks your understanding of the two essential attributes that must be specified for numbers used in arithmetic operations inside processors, digital signal processors, and arithmetic-logic units.

Given Data / Assumptions:

• Numbers are represented in a positional binary format inside digital hardware.
• Arithmetic operations require unambiguous interpretation of the operands.
• The context could be signed magnitude, 2’s complement, 1’s complement, or other signed schemes.

Concept / Approach:
Two independent properties define a signed numeric quantity: the sign (positive or negative) and the magnitude (the absolute size). Binary formats encode these in different ways. Signed-magnitude uses a dedicated sign bit plus magnitude bits. Two’s complement embeds the sign within the most significant bit and defines a wrap-around coding for negatives, but the underlying conceptual attributes remain sign and magnitude. The radix (base) of the system is also important for interpretation, but arithmetic hardware is already designed for a fixed base (almost always base-2), so the critical per-number attributes are sign and magnitude.

Step-by-Step Solution:

Verification / Alternative check:
Consider subtraction A − B implemented as A + (−B). To form −B you need to know the sign rule and the magnitude of B; two’s complement does this by inversion plus 1, but conceptually still uses sign and magnitude.

Why Other Options Are Wrong:

Common Pitfalls:
Confusing format (e.g., two’s complement) with the conceptual attributes; assuming base must be labeled per value rather than per system.

Final Answer:
sign, magnitude