Question

The algorithm is illustrated by the division of two 4-bit unsigned integers and can be summarized as follows:

1. Double the dividend width by appending 0’s in front and align the divisor to the leftmost bit of the extended dividend.
2. If the corresponding dividend bits are greater than or equal to the divisor, subtract the divisor from the dividend bits and make the corresponding quotient bit 1. Otherwise, keep the original dividend bits and make the quotient bit 0.
3. Append one additional dividend bit to the previous result and shift the divisor to the right one position.
4. Repeat steps 2 and 3 until all dividend bits are used. Please provide a data path and FSM sketch for this design.
Assume that the divisor is stored in one register and the extended dividend is stored in two separate registers. Additionally, we request that you implement your design in VHDL(Verilog) and create test scenarios to validate its functionality.

Answer 1

To design a division algorithm in VHDL (Verilog) for two 4-bit unsigned integers, one needs to create a data path with registers for the divisor and extended dividend, an ALU for subtraction, and a shift register. An FSM controls the operations. Testbenches are used to validate the algorithm's functionality.

Step-by-step explanation:

Designing a Division Algorithm Data Path and FSM in VHDL (Verilog)The division of two 4-bit unsigned integers using an algorithm can be implemented in VHDL (Verilog) by creating a data path that supports the required operations and a finite state machine (FSM) that controls the flow of the algorithm. The data path would consist of two registers for the extended dividend and one for the divisor as stated. The FSM is responsible for managing the iteration steps, performing the comparison, and shifting operations of the divisor and the dividend.

The FSM sketch would show states for initializing the algorithm, comparing dividend bits with the divisor, subtracting if necessary, shifting the registers, and ending the calculation once all bits are processed.Implementing this design in VHDL (Verilog) requires knowledge of the language syntax to create modules for the data path and FSM, set up the initial conditions, and define the process flow. Writing testbenches is essential for validating the functionality by providing various scenarios of dividends and divisors to ensure the algorithm performs as expected in all cases.