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

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 NAND gates needed to build the XOR function shown?

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

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

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(0, 1, 3, 4, 5, 9, 12, 13, 14). How many sum terms (factors) N does it have?

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

Find the minimal SOP form of F(A, B, C, D) = Σm(8, 10, 13, 14) + d(1, 6, 7, 15), where d marks the don't-care conditions. How many product terms N does it have?

A 4-bit shift register Q₃Q₂Q₁Q₀ holds 1001. 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 1, 1, 1, 0 at the 4 edges. Give the final state Q = Q₃Q₂Q₁Q₀ as a decimal number.