How many states does a 3-bit binary counter have?
The correct answer is C: 8. The number of states a 3-bit binary counter has is 8. A 3-bit counter can represent 2³ = 8 different states (000, 001, 010, 011, 100, 101, 110, 111). For amateur radio operators, this is fundamental digital logic. Understanding this helps when working with counters.
Exam Tip
3-bit counter states = 8. Think '3'-bit = '2'³ = '8' states. A 3-bit counter can represent 2³ = 8 different states. Not 3, not 6, not 16 (4-bit) - just 8.
Memory Aid
"3-bit counter states = 8. Think '3'-bit = '2'³ = '8' states. A 3-bit counter can represent 2³ = 8 different states. Fundamental binary counting: n bits = 2ⁿ states."
Real-World Application
A 3-bit binary counter: It can count from 000 to 111, representing 8 different states (0-7 in decimal). Each bit can be 0 or 1, so 2³ = 8 possible combinations. This is fundamental binary counting - n bits = 2ⁿ states.
Key Concepts
Why Other Options Are Wrong
Option A (3): Incorrect. 3 states is too few - a 3-bit counter has 2³ = 8 states, not 3. Calculation error.
Option B (6): Incorrect. 6 states is too few - a 3-bit counter has 2³ = 8 states, not 6. Calculation error.
Option D (16): Incorrect. 16 states is for a 4-bit counter (2⁴ = 16), not 3-bit. 3-bit has 2³ = 8 states.
题目解析
The correct answer is C: 8. The number of states a 3-bit binary counter has is 8. A 3-bit counter can represent 2³ = 8 different states (000, 001, 010, 011, 100, 101, 110, 111). For amateur radio operators, this is fundamental digital logic. Understanding this helps when working with counters.
考试技巧
3-bit counter states = 8. Think '3'-bit = '2'³ = '8' states. A 3-bit counter can represent 2³ = 8 different states. Not 3, not 6, not 16 (4-bit) - just 8.
记忆口诀
3-bit counter states = 8. Think '3'-bit = '2'³ = '8' states. A 3-bit counter can represent 2³ = 8 different states. Fundamental binary counting: n bits = 2ⁿ states.
实际应用示例
A 3-bit binary counter: It can count from 000 to 111, representing 8 different states (0-7 in decimal). Each bit can be 0 or 1, so 2³ = 8 possible combinations. This is fundamental binary counting - n bits = 2ⁿ states.
错误选项分析
Option A (3): Incorrect. 3 states is too few - a 3-bit counter has 2³ = 8 states, not 3. Calculation error. Option B (6): Incorrect. 6 states is too few - a 3-bit counter has 2³ = 8 states, not 6. Calculation error. Option D (16): Incorrect. 16 states is for a 4-bit counter (2⁴ = 16), not 3-bit. 3-bit has 2³ = 8 states.
知识点
3-bit binary counter, 8 states, Binary counting, Digital logic
Verified Content
Question from official FCC General Class question pool. Explanation reviewed by licensed amateur radio operators.