1. Express the following Boolean functions in the canonical sum-of-products (SOP) using minterms, or the canonical product-of-sums (POS) form using maxterms, as indicated.

(a). Express f (x, y, z) = ( x · z) + ( x · y) + ( x · y) as a canonical SOP

(b). Express f (x, y, z) = ( x · y) + ( x · y · z) + ( x · z) + ( y · z ) as a canonical SOP

(c). Express f (x, y, z) = ( y + z ) · ( x + y ) · ( x + y ) as a canonical POS.

(d). Express f (x, y, z) = ( x + z ) · ( x + y ) as a canonical POS.

2. Use Boolean Algebra to minimize the following canonical forms into the standard POS or SOP form as indicated, and calculate the cost

(a). Find the lowest cost standard SOP equivalent of f(x, y, z) = m2 + m5 + m6 + m7.

(b). Find the lowest cost standard POS equivalent of f(x, y, z) = M1M2M4M5M6.

(c). Find the lowest cost standard SOP equivalent of f(x, y, z) = m0 + m1 + m3 + m6.

(d). Find the lowest cost standard SOP equivalent of f(x, y, z) = m0 + m2 + m4 + m5.

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