Numeration for digital electronics — Evaluate: “Digital electronics must use a numbering system that has more than ten digits.”
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AIncorrect
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BCorrect
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CValid only for octal and hex machines
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DApplies to analog computers only
Answer
Correct Answer: Incorrect
Explanation
Introduction / Context: Digital electronics are fundamentally binary—two symbols (0 and 1) suffice to represent any number or code by positional weighting. Higher-radix notations such as octal and hexadecimal are conveniences for humans, not necessities for the hardware. The statement claims that a system must use a base with more than ten digits, which is not accurate.Given Data / Assumptions:
- Binary digits (bits) are the native storage and processing units.
- Human-readable notations (octal/hex/decimal) are for documentation and debugging.
- Logic families implement two distinct levels for robustness.
Concept / Approach: With positional notation, any integer can be represented with any base b ≥ 2. Hardware favors b = 2 due to physical reliability of two-state devices and simple logic. While base-10 displays are common for user interfaces, internals remain binary. Therefore, it is false that digital electronics must have “more than ten digits.”Step-by-Step Solution:
Recognize that binary (base 2) is sufficient and standard.Note that octal (base 8) and hex (base 16) are optional notations for compactness.Conclude the necessity claim is incorrect.Verification / Alternative check:
Consider microcontrollers and CPUs; all store and compute using bits while exposing decimal UX only at the periphery.Why Other Options Are Wrong:
Correct: Would imply bases greater than 10 are mandatory, which is untrue.Valid only for octal and hex machines: No such requirement exists; radix choice for representation is flexible.Applies to analog computers only: Analog computing does not use positional digit systems.Common Pitfalls:
Confusing machine-native representation (binary) with human shorthand (hex/oct).Believing multiple voltage levels (multi-valued logic) are required; they are rare and not necessary.Final Answer:
Incorrect