**How many NAND gates are needed to implement a full adder? **

Hint: Use the Boolean expression for the sum and carry outputs.

**Design a 4-bit binary counter using D flip-flops.**

Hint: Use the output of one flip-flop as the clock input for the next one.

**Implement a 4-to-1 multiplexer using only NOR gates. **

Hint: Use De Morgan's laws to convert the AND-OR implementation to NOR-NOR.

**Design a circuit that takes a 3-bit input and outputs 1 if the input is a prime number and 0 otherwise.**

Hint: Use a Karnaugh map to simplify the Boolean expression.

**Implement a JK flip-flop using a T flip-flop and some logic gates. **

Hint: Use the feedback loop of the T flip-flop to control its toggle function.

**Design a circuit that takes two 4-bit inputs A and B and outputs 1 if A is greater than B, 0 if A is equal to B, and -1 if A is less than B. **

Hint: Use a magnitude comparator and some logic gates.

**Implement a shift register that can perform left, right and parallel shifts using D flip-flops and multiplexers. **

Hint: Use multiplexers to select between different inputs for each flip-flop.

**Design a circuit that can generate a Fibonacci sequence using an up-counter, an adder and some registers. **

Hint: Use two registers to store the previous two terms of the sequence and update them after each count.

**Implement a 7-segment decoder that can display the hexadecimal digits 0-F using logic gates. **

Hint: Use a truth table to find the Boolean expressions for each segment.

**Design a circuit that can perform binary multiplication of two 4-bit numbers using adders and shift registers. **

Hint: Use a shift-and-add algorithm to multiply the numbers.

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