Assume that (X)10 is represented as a 4-bit unsigned binary number (A3A2A1A0)2. Further assume that we have two functions f1=sin(X*π/8)+0.5 and f2= cos(X*π/8). We define the following function G(A3, A2,A1,A0): G=1 if f1f2>0; G=0 if f1f2<0; G can be either 1 or 0 when f1f2=0: (1) Please show the minterm expansions G. You need to show the key process of obtaining your results (2) Obtain the simplified SOP (sum of products) of G via K-map reduction, and implement it with a two-level AND-OR circuit. (3) Obtain the simplified POS (product of sums) of G via K-map reduction, and implement the result with a two-level OR-AND circuit.
Assume that (X)10 is represented as a 4-bit unsigned binary number (A3A2A1A0)2. Further assume that we have two functions f1=sin(X*π/8)+0.5 and f2= cos(X*π/8). We define the following function G(A3, A2,A1,A0): G=1 if f1f2>0; G=0 if f1f2<0; G can be either 1 or 0 when f1f2=0:
(1) Please show the minterm expansions G. You need to show the key process of obtaining your results
(2) Obtain the simplified SOP (sum of products) of G via K-map reduction, and implement it with a two-level AND-OR circuit.
(3) Obtain the simplified POS (product of sums) of G via K-map reduction, and implement the result with a two-level OR-AND circuit.
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Assume that (X)10 is represented as a 4-bit unsigned binary number (A3A2A1A0)2 . Further assume that we have two functions f1=sin(X*π/8)+0.5 and f2= cos(X*π/8). We define the following function G(A3, A2,A1,A0): G=1 if f1f2>0; G=0 if f1f2<0; G can be either 1 or 0 when f1f2=0:
(1) Please show the minterm expansions G. You need to show the key process of obtaining your results
(2) Obtain the simplified SOP (sum of products) of G via K-map reduction, and implement it with a two-level AND-OR circuit.
(3) Obtain the simplified POS (product of sums) of G via K-map reduction, and implement the result with a two-level OR-AND circuit.
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