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

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

1. 1N1
2. 2N2
3. 3G1
4. 4G2
5. 5G3

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 XNOR function shown?

Simplify F = BC′ + ABC + A′C to its minimal sum-of-products form. How many literals L does the simplified expression contain?

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

A 4-bit shift register Q₃Q₂Q₁Q₀ holds 1011. At every clock edge the bits shift one place to the right (Q₃ → Q₂ → Q₁ → Q₀, Q₀ is lost) and the serial input enters Q₃. The serial input is 0, 1, 0, 0, 0 at the 5 edges. Give the final state Q = Q₃Q₂Q₁Q₀ as a decimal number.

Find the minimal SOP form of F(A, B, C, D) = Σm(3, 4, 5, 6, 8, 9, 10, 13, 14, 15) + d(0, 1, 11), where d marks the don't-care conditions. How many product terms N does it have?