## NAND Gate and Logical Networks

### Objective:

To show that the NAND gate is a complete gate and to analyze logical networks

### Introduction:

In the previous experiment, all the basic logic gates were studied. A set of gates necessary to implement every Boolean function is a complete set. AND, OR and INVERTER make a complete set. NAND is also a complete set.

### Procedure:

Show a network of NAND gates to function as:

- INVERTER
- 2-input AND
- 2-input OR

Wire up the circuits and verify their operations.

#### Decimal to Binary Encoder:

To communicate with a computer, it is necessary to convert input information
into a binary form that the computer understands. One device that does this
translation is an encoder. An encoder is a device that has 2^{n} (or fewer)
inputs and n outputs. The outputs generate the binary version of the inputs.
Figure 1 shows an encoder for converting the decimal digits 0 to 7 to their
binary equivalents. Construct this encoder.

Figure 1 - Binary Encoder using NAND gates

- Set all switches to 1 Observe and record the condition of the LED's.
- Reset switch 1 to level (0), observe and record the condition of the LED's.
- Set switch 1 to level (1) and reset switch 2 to (0), observe and record the conditions of the LED's.
- Continue setting one switch at a time and record the indication of the LED's. Demonstrate your circuit to the instructor.
- Explain the operation of the encoder used by explaining the operation of each gate.
- Design (on paper only) an encoder to convert the decimal numbers 0 to 15 into binary.

#### Decoder:

When a computer has completed an operation, the answer is usually given
in binary form that is required to be decoded to decimal form for most people.
A decoder could do this function. It has n inputs and 2^{n} outputs. A decoder using NAND gates is shown
below. Construct this decoder.

- Analyze the above circuitry by constructing the truth table. Explain how the logic elements operate.
- With all switches in 0 position, observe and record the LED outputs.
- Switch in all possible combinations of the input switches. Observe and record the LED outputs. Compare it with the truth table constructed. Demonstrate your circuit to the instructor.
- Design (on paper only) the circuitry to decode the binary numbers up to 1111 into decimal.