2.5 Describing Logic Circuits Algebraically

Any logic circuit, no matter how complex, may be completely described using the Boolean operations previously defined, because the OR gate, AND gate, and NOT gate are the basic building blocks of digital systems. Any logic function can be represented in a truth table. The number of rows in the table is 2ⁿ where n is the number of binary variables in the function.

Example no 1.

Write the Boolean expression for the logic circuit given below.

Figure 1 Logic Circuit Example 1

Solution no 1.

Figure 2 Solution in example no 1

Determining the intermediate outputs for the AND and inverter gates before writing the expression for the final output which is Y=AB+C’.

Example no 2.

Write the Boolean expression for the logic circuit given below.

Figure 3 Logic Circuit Example 2

Figure 4 Solution in example no 2

Final answer is X=(AB)’+CD