ENI713- Combinational logic gates

Boolean Algebra Laws and Rules

1- The Commutative Law: A + B = B +A A .B = B .A 2-The Associative Law: A + (B + C) = (A + B) + C A . (B . C) = (A . B) . C 3-The Distributive Law A . (B + C) = (A . B) + (A . C) A + (B . C) = (A + B) . (A + C) ̅̅̅̅

Conversion from Boolean Expression to Logic Circuit

1. Determine how many inputs the circuit has. 2- Draw a line to represents each of the inputs as shown

3.5 Circuit Simplification Using Boolean Algebra

A simplified logic circuit uses a fewer number of gates, is simpler to construct, consumes less power and therefore costs less to construct and run.

Now share your screen and use your multisim simulation to build XOR Logic circuit

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There are 3 ways to represent combinational logic functions

Boolean Algebra Truth table Logic Circuit

Logic Circuit and Symbol

Referring to the logic circuit in Figure 18, you can see that an XOR gate is made of the combination of AND, OR, and NOT gates. The standard symbol for the XOR gate is shown in the Figure . Note that the XOR gate has only two inputs.

Share your screen and draw the NAND logic circuit on multisim

Share your circuit with your team on MS teams

XOR Logic Gate

The logical operation of XOR is such that the output is high only when the two inputs are at opposite levels.

Logic Operation and Truth Table

The logical operation of the NAND gate is such that a LOW output occurs only when all inputs are HIGH. When any of the inputs are LOW, the output will be HIGH. The truth table illustrating the logical operation of a two input NAND gate for all input combinations is shown in

NAND Logic Gate

The term NAND is a short form of NOT-AND and means an AND function with inverted output. A standard logic symbol for a two-input NAND gate and its equivalent to an AND gate followed by a NOT gate (inverter), , with the inputs labeled A and B and the output labeled X. The bubble indicate an inverted output.

NOR Logic Gate

The term NOR is a short form of NOT-OR and is equivalent to an OR function with inverted output. The standard logic symbol for a two-inputs NOR gate, and its equivalent to an OR gate followed by a NOT gate (inverter), are shown in Figures , with the inputs labeled A and B and the output labeled X. The bubble indicates an inverted output.