Figure 4-71 shows a BCD counter that produces a four-bit output representing the BCD code for the number of pulses that have been applied to the counter input. For example, after four pulses have occurred, the counter outputs are DCBA = 0100₂ = 4₁₀. The counter resets to 0000 on the tenth pulse and starts counting over again. In other words, the DCBA outputs will never represent a number greater than 1001₂ = 9₁₀.

(a)* Design the logic circuit that produces a HIGH output whenever the count is 2, 3, or 9. Use K mapping and take advantage of the don’t-care conditions.

(b) Repeat for x = 1 when DCBA = 3, 4, 5, 8.

Figure 4-71

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non BCD counter D (MSB) с B A Logic circuit X HIGH only when DCBA 210, 310, or 910