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Hardware interview practice

Implement a constant multiply without truncation

MediumRTL ArithmeticSystemVerilog

For an unsigned 10-bit input, implement y = 9*x + 3 without using the multiplication operator and choose an expression width that preserves the maximum result.

Starting point

Question code

input  logic [9:0]  x;
output logic [13:0] y;
Reviewed example

Work through one case

Input
x = 10'd1023
Expected output
y = 14'd9210

The maximum input produces 9*1023 + 3 = 9210, which is below 2^14 and therefore fits losslessly in 14 bits.

What to cover

Requirements

  1. Implement 9*x as (x << 3) + x.
  2. Extend x before shifting so every intermediate is 14 bits wide.
  3. Add the constant 3 without truncation.
  4. State and verify the maximum possible result.
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