Define Fan-out and Figure of merit. Compare TTL, ECL and CMOS logic families. What is Decoder? Explain how combinational circuits like full adder can be implemented with decoder.

1. Fan-out and Figure of Merit:

Fan-out:

• The fan-out of a logic gate is the maximum number of inputs that can be connected to its output without degrading its performance.
• It is limited by the current-sinking capability of the output transistor.
• For example, if a gate has a fan-out of 10, it can drive up to 10 inputs without any problems.

Figure of Merit:

• The figure of merit (FOM) of a logic family is a measure of its overall performance.
• It is calculated by dividing the propagation delay by the power consumption:

FOM = Propagation delay / Power consumption

• A higher FOM indicates better performance.

2. Comparison of TTL, ECL and CMOS Logic Families:

TTL (Transistor-Transistor Logic):

• TTL is a widely used logic family that is known for its low cost and high speed.
• It uses bipolar transistors as its basic building blocks.
• TTL gates have a relatively high fan-out and a moderate FOM.

ECL (Emitter-Coupled Logic):

• ECL is a high-speed logic family that is used in applications where speed is critical.
• It uses emitter-coupled transistors as its basic building blocks.
• ECL gates have a very high fan-out and a high FOM.
• However, ECL is also more expensive and power-hungry than TTL.

CMOS (Complementary Metal-Oxide-Semiconductor):

• CMOS is a low-power logic family that is widely used in portable devices.
• It uses complementary pairs of MOSFETs as its basic building blocks.
• CMOS gates have a very high fan-out and a very high FOM.
• However, CMOS is also more complex to design and manufacture than TTL and ECL.

3. Decoder:

• A decoder is a combinational circuit that converts a binary code into a set of outputs, where each output represents a specific bit in the code.
• Decoders are used in a variety of applications, such as address decoding in memory systems and input decoding in control circuits.

4. Implementation of Full Adder using Decoder:

• A full adder is a combinational circuit that adds two binary digits and a carry-in to produce a sum and a carry-out.
• It can be implemented using a decoder as follows:

1. The two binary digits are decoded into four outputs, each of which represents a specific combination of the two bits.
2. The carry-in is also decoded into two outputs, one for the carry-in and one for the inverted carry-in.
3. The sum and carry-out are then generated using a truth table.

• The following table shows the truth table for a full adder:

| A | B | Carry-in | Sum | Carry-out |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |

• The following figure shows a circuit diagram for a full adder implemented using a decoder:

[Circuit Diagram of Full Adder Implemented Using Decoder]

• The decoder in this circuit is a 3-to-8 decoder, which means that it has three inputs and eight outputs.
• The two binary digits are connected to the inputs of the decoder, and the carry-in is connected to the control input of the decoder.
• The outputs of the decoder are connected to the inputs of the sum and carry-out gates.
• The sum and carry-out gates are implemented using AND gates and OR gates.