Computer number systems – internal calculation base In digital electronics and computer architecture, computers represent and calculate numbers using which fundamental numeral system at the hardware level (logic gates, ALUs, memory cells)?

Introduction / Context:
Understanding how computers represent data is essential for programming, digital logic, and troubleshooting. Although humans commonly use base-10 (decimal), computer hardware is constructed from electronic switches that naturally implement base-2 (binary). This question checks foundational knowledge of number systems as used by processors, memory, and digital circuits.

Given Data / Assumptions:

• A “computer” here refers to the physical hardware (CPU, ALU, registers, memory).
• Logic gates operate with two stable voltage states (often labeled 0 and 1).
• We are concerned with the native representation for arithmetic and logic.

Concept / Approach:
Binary uses digits 0 and 1. Each binary digit (bit) corresponds to an “off/on” or “low/high” state realizable with transistors. Larger units (nibbles, bytes, words) are sequences of bits. Arithmetic units implement binary addition, subtraction, multiplication, and division using combinational and sequential logic (full adders, shifters, multipliers). Decimal or octal may be used for human-friendly display, but internally the encoding is binary (with special encodings like two’s complement for signed integers and IEEE-754 for floating point).

Step-by-Step Solution:
Identify the physical substrate: transistors that switch between two states.Match two states to base-2 representation → binary digits 0 and 1.Conclude that all arithmetic and logical operations are performed in binary, even if results are shown to users in decimal or hexadecimal.

Verification / Alternative check:
Examine CPU instruction set manuals: opcodes manipulate bits/bytes; arithmetic flags reflect binary outcomes (carry, zero, sign, overflow). Memory addresses and data buses are also binary lines.

Why Other Options Are Wrong:

• Decimal: sometimes emulated (e.g., BCD instructions), but not the core hardware representation.
• Octal: a historical shorthand for binary on certain systems; not the internal computation base.
• None of the above: incorrect because binary is correct.

Common Pitfalls:
Confusing display base (what users see) with computation base (what hardware uses). Even when programmers write hexadecimal, it is simply a compact human representation of underlying binary bits.

Final Answer:
Binary