DescriptionQ812
Q812DesignASIC interview problem
Implement a constant multiply without truncation
TechniquesDesignSystemVerilogShift-addBit widthCombinational logic
DifficultyMedium
TopicRTL Arithmetic
LanguageSystemVerilog
Requirements4 checkpoints
01
Problem
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 declarationSystemVerilog
input logic [9:0] x;
output logic [13:0] y;Example input and output
Use this case to check your interpretationInput
x = 10'd1023Output
y = 14'd9210Explanation
The maximum input produces 9*1023 + 3 = 9210, which is below 2^14 and therefore fits losslessly in 14 bits.
02
Requirements (4)
- Implement 9*x as (x << 3) + x.
- Extend x before shifting so every intermediate is 14 bits wide.
- Add the constant 3 without truncation.
- State and verify the maximum possible result.