Digital logic: gates, K-maps & flip-flops worksheet with answers

The inputs of the logic circuit are A = 0, B = 0 and C = 1. Exactly one of its gates has the output 0. Click that gate.

1. 1N1
2. 2G1
3. 3G2
4. 4G3

NAND and NOR are universal gates: any logic function can be built from one of them alone. What is the minimum number N of 2-input NOR gates needed to build the OR function shown?

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(3, 4, 5, 6, 9, 12, 13, 14, 15). How many literals L does it contain in total (a primed variable counts as one literal)?

A 4-to-1 multiplexer has its select inputs S₁ = A and S₀ = B, and its data inputs tied to I₀ = C′, I₁ = 1, I₂ = 0, I₃ = C′. For how many of the 8 combinations of A, B and C is the output F = 1? Find N.

For F(A, B, C, D) = Σm(3, 5, 6, 12, 14, 15) + d(0, 2, 4, 7, 9, 10, 13), where d marks the don't-care conditions, find the number N of essential prime implicants.

A synchronous mod-12 counter counts 0, 1, …, 11 and then returns to 0. It starts at 6. Which count Q (in decimal) does it show after 23 clock pulses?