Question

A MOD 2 and a MOD 5 up-counter when cascaded together results in a MOD ______ counter.

• A. 3
• B. 7
• C. 10
• D. 20

Hint:

When cascading counters, the total number of unique states (the modulus) is the product of the individual moduli: \(M_{total} = M_1 \times M_2\).

Answer 1

The Correct Option is C

Step 1: Understand the principle of cascading counters. When two or more counters are cascaded, the output of the first counter is used as the clock input for the second counter, and so on.
Step 2: Determine the modulus of the resulting counter. The modulus (MOD number) of a cascaded counter is the product of the moduli of the individual counters. \[ MOD_{total} = MOD_1 \times MOD_2 \times \cdots \] In this case, we have a MOD-2 counter and a MOD-5 counter. \[ MOD_{total} = 2 \times 5 = 10 \] The resulting circuit is a MOD-10 counter, also known as a decade counter.