n stage ripple counter can count up to

2^{n}

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2^{n}

- 1

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2^{n - 1}

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Solution

The correct option is B $2^{n}$ - 1
n stage ripple counter can count up to 2^n-1.

A ripple counter is an asynchronous counter where only the first flip-flop is clocked by an external clock. All subsequent flip-flops are clocked by the output of the preceding flip-flop. Asynchronous counters are also called ripple-counters because of the way the clock pulse ripples it way through the flip-flops. The MOD of the ripple counter or asynchronous counter is 2^n if n flip-flops are used.

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x^{n} - 1 = 0, n > 1, n \in N,

1, a_{1}, a_{2}, \dots, a_{n - 1},

The value of $\sum_{r = 1}^{n + 1} (\sum_{k = 1}^{n}^{k} C_{r - 1})$ where r, k, n $ϵ$ N is equal to

(1 + x)^{n} = n \sum r = 0^{n} C_{r} x^{n},

\frac{C_{0}}{1 \cdot 2} 2^{2} + \frac{C_{1}}{2 \cdot 3} 2^{3} + \frac{C_{2}}{3 \cdot 4} 2^{4} + \dots + \frac{C_{n}}{(n + 1) (n + 2)} 2^{n + 2}

\frac{^{n} C_{0}}{2^{n}} + 2. \frac{^{n} C_{1}}{2^{n}} + 3. \frac{^{n} C_{2}}{2^{n}} + \dots . (n + 1) \frac{^{n} C_{n}}{2^{n}} = 16

n

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