Question

Design a dedicated register file architecture that computes M=4x²yz+6xyz+9yz+4z+7 using minimal number of registers and minimal number of clock cycles. You may use at most one ALU, at most one multiplier, and any counter. Minimize your hardware. You may assume you can read and write to registers in same cycle.

The opcodes for ALU are:
1. 01 corresponds to +
2. 10 corresponds to -
3. 00 corresponds to increment of the left input (ignores right input). Please design both data path and control logic.

Answer 1

The dedicated register file architecture is designed by breaking down the equation into parts, using pipelining to compute terms in parallel, and reusing intermediate values to minimize the total number of registers and clock cycles required.

Step-by-step explanation:

Data Path and Control Logic Design

To design a dedicated register file architecture to compute M=4x²yz+6xyz+9yz+4z+7 with minimal resources, the following steps should be taken. It's important to break down the equation into parts that can be efficiently computed using a single ALU and a single multiplier. The terms can be grouped and calculated step by step:

1. Compute x² and store it in a register.
2. Multiply x² by 4y and store the result.
3. Add the result to 6xy multiplied by z and store the new result.
4. Add 9y multiplied by z to the previous result and store it.
5. Add 4z to the computed value and store it again.
6. Add the constant 7 to the above total to get M.

Control logic can be implemented using a finite state machine that sequences through the operations as described above for each term of the equation. This logic will control the data path components (registers, ALU, multiplier, counters) at each step.

The sequence of operations must be designed to minimize the number of clock cycles. For instance, while the ALU is computing a sum, the multiplier can simultaneously compute a product for the next step. Therefore, pipelining can be employed here to overlap operations and reduce the overall number of cycles needed.

Registers would need to hold intermediate values between operations, and to optimize the design, some of these values can be reused to minimize the total number of registers required. For example, a temporary register can hold the value of xyz, which can be scaled by 6 in the second step and added to the 4x²z in the first step.