Question

Boolean function (𝑥, 𝑦, 𝑧) is given by formula represented in the table below.

• Represent the formula for the function (𝑥, 𝑦, 𝑧) in graphical form (i.e. by circuit). Find the depth of the formula as the height of binary tree constructed for its calculation.
• Construct value table (truth table) for the function 𝑓(𝑥, 𝑦, 𝑧)
• Construct PDNF and PCNF for the function (𝑥, 𝑦, 𝑧) with a help of its value table. Find lengths of these PDNF and PCNF. 4) Construct ANF (Zhegalkin polynomial) for the function (𝑥, 𝑦, 𝑧) with a help of its PDNF or using undefined coefficient method. Determine essential and fictitious variables of the function (𝑥, 𝑦, 𝑧).

 .                  𝑓(𝑥, 𝑦, 𝑧) = ((𝑧 → (𝑥 → 𝑧)) ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ↔ 𝑦) ∨ ((𝑥 → ̅𝑧 ) & (𝑧 → 𝑥))