# Assignment 4

Name - Tilak Reddy
Roll No. - CS22B047

## Logic Operations
### Bitwise operations
NAND and NOR are universal gates. So, if we can design these gates rest all gates can be designed form them.The proposed truth table for these operations is given below.
#### Truth table for ternary NAND gate:
| Input 1 | Input 2 | NAND | NOR |
|---------|---------|------|-----|
|0|0|2|2|
|0|1|2|1|
|0|2|2|0|
|1|0|2|1|
|1|1|1|1|
|1|2|1|0|
|2|0|2|0|
|2|1|1|0|
|2|2|0|0|

### Ternary Full adder
A full adder is nothing but XOR operations on 3 inputs.We can easily derive logic for XOR from truth table proposed for NAND and NOR.

#### Truth table for Full Adder:

| A | B | cin | cout | sum |
|---|---|-----|------|-----|
|0|0|0|0|0|
|0|0|1|0|1|
|0|0|2|0|2|
|0|1|0|0|1|
|0|1|1|0|2|
|0|1|2|1|0|
|0|2|0|0|2|
|0|2|1|1|0|
|0|2|2|1|1|
|1|0|0|0|1|
|1|0|1|0|2|
|1|0|2|1|0|
|1|1|0|0|2|
|1|1|1|1|0|
|1|1|2|1|1|
|1|2|0|1|0|
|1|2|1|1|1|
|1|2|2|1|2|
|2|0|0|0|2|
|2|0|1|1|0|
|2|0|2|1|1|
|2|1|0|1|0|
|2|1|1|1|1|
|2|1|2|1|2|
|2|2|0|1|1|
|2|2|1|1|2|
|2|2|2|2|0|

## Instruction Encoding

To devise an efficient encoding scheme for ternary instructions, we'd want to optimize both the representation of instructions and their execution. Here's a proposed encoding scheme:

#### Opcode Design:
Use a compact opcode format that indicates the operation type and addressing modes. Since ternary logic encompasses arithmetic, bitwise, and logical operations, allocate opcode bits to represent these categories. For example:
- Bits [0-1]: Operation type (e.g., 00 for arithmetic, 01 for bitwise, 10 for logical).
- Bits [2-4]: Addressing mode for Operand A.
- Bits [5-7]: Addressing mode for Operand B.
- Bits [8-10]: Addressing mode for Operand C.

#### Operand Encoding:
Since ternary logic involves three possible values (0, 1, 2), each operand can be represented using a small number of bits. For example:
Use 2 bits for each operand to represent values 0, 1, and 2.

#### Addressing Modes:
Support various addressing modes like immediate, register, and memory addressing for operands. Allocate specific bits in the instruction to specify the addressing mode for each operand.

#### Instruction Length:
Aim for fixed-length instructions to simplify decoding. This ensures uniform instruction fetching and decoding.

#### Efficient Use of Opcode Space:
Assign opcodes to frequently used instructions and operations that represent common tasks. Leave room for future expansion or special instructions.

#### Decoding Logic:
Design efficient decoding logic that can quickly interpret the encoded instructions. Use bit manipulation techniques to extract opcode fields and operand values efficiently.

#### Alignment:
Align instructions to natural boundaries to facilitate efficient memory access and decoding.

#### Special Instructions:
Introduce special instructions for commonly used operations or sequences to optimize performance in specific scenarios.

## Pipeline

Adapting a pipeline architecture to accommodate ternary logic involves several considerations to leverage the benefits of ternary operations efficiently. Here's how the pipeline architecture might be adjusted:

#### Instruction Fetch Stage:
Modify the instruction fetch unit to handle ternary instructions. This includes fetching ternary instructions from memory and decoding them into their respective operation types and operands.

#### Instruction Decode Stage:
Enhance the instruction decoder to interpret ternary instructions, extract opcode fields, and decode addressing modes for operands. This stage must be able to handle the compact opcode format designed for ternary instructions.

#### Execution Units:
Introduce specialized execution units capable of performing ternary arithmetic, bitwise, and logical operations. These units should support ternary operands and produce ternary results efficiently.

#### Data Paths:
Adjust the data paths to accommodate ternary operands and results. This may involve widening the data paths to support ternary values (0, 1, 2) or introducing specialized ternary data paths alongside existing binary ones.

#### Pipeline Stages:
Potentially introduce additional pipeline stages to handle the unique characteristics of ternary operations. For example, stages dedicated to ternary operation execution, result calculation, and forwarding.

#### Hazard Detection and Forwarding:
Enhance hazard detection and forwarding mechanisms to handle dependencies and hazards arising from ternary instructions. This ensures efficient execution without stalls or data hazards.

#### Memory Access:
Adapt memory access units to support ternary data if needed. This may involve modifications to memory interfaces and data buses to handle ternary values during loads and stores.

#### Control Logic:
Adjust control logic to manage the flow of ternary instructions through the pipeline, including branch prediction, speculative execution, and exception handling.

#### Testing and Validation:
Develop thorough testing procedures to validate the functionality and performance of the modified pipeline architecture with ternary logic. This includes verifying correctness, throughput, and latency under various conditions.

#### Optimization Opportunities:
Explore optimization opportunities specific to ternary logic, such as exploiting parallelism inherent in ternary operations or minimizing energy consumption through efficient ternary arithmetic.

## Address range and capacity

Implementing a ternary addressing system can indeed exponentially increase the addressable memory space compared to a binary system. Here's how it could be done, along with considerations for physical memory size and access speed:

#### Ternary Addressing System:
In a ternary addressing system, each address line can have three possible states (0, 1, 2) instead of just two (0, 1) in a binary system.
With n ternary address lines, the total addressable memory space becomes 3^n instead of 2^n in a binary system. This exponential increase allows for significantly larger memory capacity.

#### Physical Memory Size:
Implementing a ternary addressing system requires additional hardware support to handle ternary addresses. This includes ternary address decoders, multiplexers, and memory cells capable of storing ternary values.
The physical memory size needs to be increased to accommodate the larger addressable space. However, the actual increase depends on the number of ternary address lines and the memory organization.
Ternary memory cells can store ternary values (0, 1, 2) instead of binary values (0, 1), which requires modifications to memory cell design and storage mechanisms.

#### Memory Organization:
Ternary memory organization can vary based on the specific requirements of the system. It can include flat memory models, hierarchical memory structures, or specialized memory architectures optimized for ternary addressing.
Efficient memory organization is essential to maximize the utilization of the expanded addressable space while maintaining access speed and minimizing latency.

#### Access Speed:
Access speed in a ternary memory system depends on various factors, including memory technology, access mechanisms, and memory organization.
Ternary memory access may introduce additional complexity compared to binary memory access due to the increased number of address states and memory cell configurations.
Access speed can be affected by factors such as memory latency, bus contention, and access patterns. Optimizing memory access algorithms and hardware design is crucial to ensure efficient access speed.

#### Trade-offs:
Implementing a ternary addressing system offers the advantage of exponentially increasing the addressable memory space.
However, it comes with trade-offs such as increased hardware complexity, higher implementation costs, and potentially slower access speed due to additional processing overhead.
Balancing these trade-offs is essential to ensure that the benefits of the expanded memory capacity outweigh the associated drawbacks.