Consider an example,

### Example 1:

F = x + y’z is the given function. Show the result in truth table and draw a logic diagram using only NAND gate.

### Solution:

Given function F = x + y’z is *combinational circuit ,*meaning it takes input and produce output and does not store any bit information.

There are three variable in this function then we will draw a 3 variable Truth Table for this function.

Truth Table |

Next we will implement the function using **NOT-AND-OR** gate .

Logic Diagram |

**F = x + y’z**uses only two gates – an

**OR**gate and an

**AND**gate.

**CONVERT TO NAND CIRCUIT**

**NOT-OR-AND**circuit we need to change the

**AND**gate and

**OR**gate to

**NAND**equivalent.

This is shown below,

NAND implementation using AND and OR gate |

**NAND Gate construction using AND gate**

*F = (x . y)’*

**NAND Gate construction using OR gate**

*F = ( x’ + y’) = (x . y)’*

In the above diagram, the **AND** is converted into a **NAND **by adding a complement to the output. Similarly, **OR **gate is converted into a **NAND **equivalent gate by complementing both the inputs.

In the following diagram, I have implemented **F= X + Y’Z** using **NAND** equivalent circuit.

NAND Circuit |

The output of the function should be same as previous circuit that’s why we need to complement the input of gates accordingly, which means the output of **F = ((Y’ . Z) . X’)**