What is the maximum possible range of bit-count specifically in n-bit binary counter consisting of ‘n’ number of flip-flops?
Answer & step-by-step solution
An n-bit binary counter has 2ⁿ distinct states. If it starts at 0, the highest count is therefore 2ⁿ − 1, giving the range 0 to 2ⁿ − 1.
Concept & Reasoning
Each flip-flop stores one binary bit, so n flip-flops form 2ⁿ unique bit patterns. A 4-bit counter, for example, runs from 0000₂ (0) to 1111₂ (15), i.e. 0 to 2⁴−1. This generalizes directly to n bits.
How to Solve It in the Exam
n bits → 2ⁿ states → maximum numeric count 2ⁿ−1.
Important Exam Point
Separate 'number of states' from 'largest count'.
Quick Trick
n bits → 2ⁿ states → maximum numeric count 2ⁿ−1.
Common Mistake
Using 2ⁿ as the maximum count instead of the number of states.
'n' फ्लिप-फ्लॉप वाले n-बिट बाइनरी काउंटर में बिट-गणना की अधिकतम संभव सीमा क्या है?
उत्तर और चरणबद्ध हल
n-बिट बाइनरी काउंटर की 2ⁿ भिन्न अवस्थाएँ होती हैं। 0 से शुरू होने पर उच्चतम गणना 2ⁿ − 1 है, अतः सीमा 0 से 2ⁿ − 1।
विस्तृत हल (मूल भाषा में)
Concept & Reasoning
Each flip-flop stores one binary bit, so n flip-flops form 2ⁿ unique bit patterns. A 4-bit counter, for example, runs from 0000₂ (0) to 1111₂ (15), i.e. 0 to 2⁴−1. This generalizes directly to n bits.
How to Solve It in the Exam
n bits → 2ⁿ states → maximum numeric count 2ⁿ−1.
Important Exam Point
Separate 'number of states' from 'largest count'.
Quick Trick
n bits → 2ⁿ states → maximum numeric count 2ⁿ−1.
Common Mistake
Using 2ⁿ as the maximum count instead of the number of states.
'n' ફ્લિપ-ફ્લોપ ધરાવતા n-બિટ બાઇનરી કાઉન્ટરમાં બિટ-ગણતરીની મહત્તમ શક્ય મર્યાદા કઈ છે?
જવાબ અને પગલાવાર ઉકેલ
n-બિટ બાઇનરી કાઉન્ટરની 2ⁿ જુદી અવસ્થાઓ હોય છે. 0 થી શરૂ થાય તો સૌથી મોટી ગણતરી 2ⁿ − 1 છે, તેથી મર્યાદા 0 થી 2ⁿ − 1.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Concept & Reasoning
Each flip-flop stores one binary bit, so n flip-flops form 2ⁿ unique bit patterns. A 4-bit counter, for example, runs from 0000₂ (0) to 1111₂ (15), i.e. 0 to 2⁴−1. This generalizes directly to n bits.
How to Solve It in the Exam
n bits → 2ⁿ states → maximum numeric count 2ⁿ−1.
Important Exam Point
Separate 'number of states' from 'largest count'.
Quick Trick
n bits → 2ⁿ states → maximum numeric count 2ⁿ−1.
Common Mistake
Using 2ⁿ as the maximum count instead of the number of states.
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