Remainder Calculator

Question

Design a​ 5-stage PipeLined​ digital system that will compute the remainder

C = A mod B

• the number A in the range from 0 to 255 (i.e., an 8-bit ​unsigned​ number)
• the number B in the range from ​8 to 15 ​(i.e., a 4-bit ​unsigned ​number with the most significant bit set to 1).
• You are​ not allowed​ to use the following operators ( mod,/,*)

Inputs

1. Clock
2. Reset (1 → asynchronous and set all registers to value of 0)
3. A : 8-bits input read at each rising edge of the clock
4. B : 4-bits input read at each rising edge of the clock
5. Start : 1 → the system will start computation.
   0 → the system will stop receiving inputs (the operations in the pipe will continue till they finish)

Outputs

1. C : 4-bits output represents the reminder
   • The First remainder value is generated after 4 clock cycles (at the 5th rising edge).
   • The rest of the results should be generated at the 6,7,8,9, ….etc. (like any normal pipeline).
2. Done: is raised to One when a valid output is generated, else 0.
3. Err : is raised to One if B value is smaller than 8 else 0

Pseudocode:

A_reg = A
B_reg = B*2^24

for i = 0 to 5
{
    if(A_reg > B_reg)
    {
        A_reg = A_reg - B_reg
    }
    B_reg = B_reg >> 1
}
C = A_reg[3 downto 0]

Simulation