Chapter B, Problem 16E

Explanation of Solution

Algorithm for Sum of Products (SOP) for AND gate:

• Design the circuit diagram using the AND gate.
• Create the truth table using the AND gate.
• Design the block diagram using truth table that includes three different inputs namely, A, B and C and one output namely, Y.
• Using the above block diagram, create another truth table.
• Calculate the SOP expression by considering the variables that has the output 1.
• Thus, the SOP expression is $\text{Y}\text{=}\text{ABC}\text{+}\text{A}\overline{\text{B}}\text{C}\text{+}\overline{\text{A}}\overline{\text{B}}\text{C}\text{+}\text{AB}\overline{\text{C}}$.
• Convert the variables using SOP expression and therefore, the SOP expression for AND gate is $\text{Y}\text{=}\overline{\text{A}}\overline{\text{B}}\overline{\text{C}}\text{+}\overline{\text{A}}\text{BC}\text{+}\text{A}\overline{\text{B}}\overline{\text{C}}$.

Algorithm for Sum of Products (SOP) for OR gate:

• Design the circuit diagram using the OR gate