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Three switching functions $f_1, \: f_2 \:$ and $f_3$ are expressed below as sum of minterms.

• $f_1 (w, x, y, z) = \sum \: 0, 1, 2, 3, 5, 12$
• $f_2 (w, x, y, z) = \sum \: 0, 1, 2, 10, 13, 14, 15$
• $f_3 (w, x, y, z) = \sum \: 2, 4, 5, 8$

Express the function $f$ realised by the circuit shown in the below figure as the sum of minterms (in decimal notation).

edited | 730 views
+8

AND gate is nothing but the INTERSECTION operation and OR gate is UNION operation...

So, F1  AND  F2 = F1 ∩ F2

={0,1,2,3,5,12 }   ∩  {0,1,2,10,13,14,15 }

={0,1,2 }

This output will goes to input to the OR gate, let say its name is F4={0,1,2 }

Now, F4 OR F3  = F4 ∪ F3

={0,1,2 } ∪ {2,4,5,8 }

={0,1,2,4,5,8}

+1
superb

Final output $= \sum 0,1,2,4,5,8$

• $f_1(w,x,y,z) = \sum 0,1,2,3,5,12$
• $f_2(w,x,y,z) = \sum 0,1,2,10,13,14,15$
• $f_3(w,x,y,z) = \sum 2,4,5,8$

$f1\text{ AND }f_2$ will give the common minterms - $f_{12} =\sum 0,1,2.$

Now $f_{12} \text{ OR } f_3 = \sum 0,1,2,4,5,8.$

by Boss (20k points)
edited by