The output of a digital circuit (y) is given by this expression y = (A | Physics 2081

Physics20815 marksNumerical: digital logic circuitUniversal gates

The output of a digital circuit (y) is given by this expression $y = (AB + \overline{C}BA)(B + C)$ Where A, B and C represent inputs. Draw a circuit of above equation using OR, AND and NOT gate and hence find its truth table. [5+0]

Boolean expression: $y = (AB + \bar{C}BA)(B + C)$ Inputs: $A$ , $B$ , $C$ Gates allowed: OR, AND, NOT The first bracket: $AB + \bar{C}BA = AB + AB\bar{C} = AB(1 + \bar{C}) = AB$ (using $1 + \bar{C} = 1$ ) So: $y = AB(B + C)$ Expand: $y = AB\cdot B + AB\cdot C = ABB + ABC$ Since

Boolean expression: $$y = (AB + \bar{C}BA)(B + C)$$ Inputs: $A$, $B$, $C$ Gates allowed: OR, AND, NOT The first bracket: $$AB + \bar{C}BA = AB + AB\bar{C} = AB(1 + \bar{C}) = AB$$ (using $1 + \bar{C} = 1$) So: $$y = AB(B + C)$$ Expand: $$y = AB\cdot B + AB\cdot C = ABB + ABC$$ Since

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The output of a digital circuit (y) is given by this expression y = (AB + overlineCBA)(B + C) Where A, B and C represent inputs. Draw a circuit of above equation using OR, AND and NOT gate and hence find its truth table. [5+0]