Binary number system basics: “The two binary digits are 1 and 2.” Assess this statement for correctness.
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ACorrect
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BIncorrect
Answer
Correct Answer: Incorrect
Explanation
Introduction / Context:The binary number system underpins all digital electronics and computing. It is essential to recall exactly which symbols (digits) are valid in base-2.
Given Data / Assumptions:
- Binary is base-2.
- Digits allowed in base-b are 0 through b-1.
- We check the claim that the binary digits are 1 and 2.
Concept / Approach:For base-2, the allowed digits are 0 and 1. The digit “2” is not valid in base-2 representation; encountering it indicates either a base-10 interpretation or an error. Digital logic physically encodes these digits as distinct states, typically low and high voltages.
Step-by-Step Solution:
Recall definition: base-b uses digits 0..(b-1).Apply to b = 2 → digits are 0 and 1 only.Identify error: “2” is outside the valid set for binary.Conclude that the statement is incorrect.Verification / Alternative check:Examples like 1011₂ show composition exclusively from 0 and 1. Attempting to write a digit “2” in binary is undefined and must be carried into the next higher bit in another radix.
Why Other Options Are Wrong:Correct: would misdefine the binary system and contradict all digital practice.
Common Pitfalls:Confusing binary digits (bits) with decimal digits; mixing radices when converting numbers.
Final Answer:Incorrect