Click the cell of the 4-variable Karnaugh map that belongs to minterm m6 (variables A, B, C, D with A the most significant bit).
The inputs of the logic circuit are A = 1, B = 0 and C = 0. Exactly one of its gates has the output 0. Click that gate.
Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(0, 1, 4, 6, 7, 8, 12, 13, 14). How many sum terms (factors) N does it have?
In this Karnaugh map exactly one 1 has no neighbouring 1, so it stays a group of one cell (a full minterm of four literals) in the minimal SOP form. Neighbours across the map edges count. Click that cell.
A 4-bit Johnson counter Q₃Q₂Q₁Q₀ starts at 0000. At every clock edge the bits shift one place to the right (Q₃ → Q₂ → Q₁ → Q₀) and Q₃ receives the inverse of Q₀. Give the state Q = Q₃Q₂Q₁Q₀ as a decimal number after 6 clock edges.
A 3-bit binary up counter starts at 5 (decimal, Q = 101). Which count Q (in decimal) does it show after 21 clock pulses?
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