Within a CPU datapath, the Arithmetic Logic Unit (ALU) performs arithmetic and logical operations primarily on which numeral system representation, as opposed to human-readable decimal?

Introduction / Context:
The Arithmetic Logic Unit (ALU) is the core computation engine of processors and digital systems. While humans often express numbers in base 10 (decimal), digital hardware operates internally on a machine-native representation optimized for logic circuitry.

Given Data / Assumptions:

• The ALU is implemented with logic gates (AND, OR, XOR, adders).
• Signals in hardware are binary (two discrete levels).
• Hexadecimal is a convenience for human representation of binary groups.

Concept / Approach:
Digital circuits encode information using bits (0/1). Adders, subtractors, shifters, and comparators are designed to manipulate bit vectors. Hex and decimal are higher-level notations; when they reach the ALU, they are already encoded as binary vectors. Therefore, the ALU processes binary numbers even if software shows hex or decimal to the user.

Step-by-Step Solution:

Verification / Alternative check:
Processor documentation specifies operand widths (e.g., 32-bit, 64-bit) and logic-level operations (bitwise ops), corroborating that computation occurs on binary words.

Why Other Options Are Wrong:

• decimal: an external representation; internally, it becomes binary-coded forms.
• hexadecimal: a compact human-friendly grouping of binary; hardware still manipulates bits.
• All of the above: only one is fundamentally true for the ALU core.
• None of the above: incorrect because binary is correct.

Common Pitfalls:
Assuming that because programmers type decimal or hex, hardware computes in those bases; overlooking encoding layers like BCD that still reduce to binary logic operations.

Final Answer:
binary