Hamming(7,4) Encoder

Verilog problems / Combinational Design

What you must build

Encode 4 data bits into a 7-bit Hamming codeword that can detect and correct any single-bit error — the error-correcting code behind ECC memory.

Engineers use “Hamming(7,4) Encoder” as a building block in combinational design. Interviewers ask for the same ports and the same corner cases this judge covers. Completing it in the browser is the same skill as writing synthesizable RTL at work, minus the EDA license.

Port contract

The judge instantiates exactly these ports. Extra ports or a different module name fail to elaborate.

How to approach this kata

This is a hard kata. Sketch the state bits and the illegal overlaps (full/empty, wrap, simultaneous enable) on paper first. A design that “usually works” in your head will fail a directed corner in the hidden tests.

Hidden tests instantiate top_module, drive the ports, and compare every sample against a golden model. They do not grade coding style. They do grade X/Z, off-by-one counters, and ignoring enables. Sign in only when you want the run saved on the leaderboard — the specification below is public.

Starter shape

Copy this skeleton into the editor (or press Reset starter). Fill the body; do not rename the module.

module top_module(
  input  [3:0] data,
  output [6:0] codeword
);

  // Your code here — p1=d1^d2^d4, p2=d1^d3^d4, p3=d2^d3^d4; codeword = {d4,d3,d2,p3,d1,p2,p1}.

endmodule

Why this shows up in interviews

Hamming(7,4) Encoder sits under Combinational Design (combinational, ecc). Concept: Three parity bits sit at positions 1, 2, and 4; each covers a different overlapping subset of the data bits ( p1=d1^d2^d4 , p2=d1^d3^d4 , p3=d2^d3^d4 ). The overlap is the whole trick — at the receiver, which parity checks fail pinpoints exactly which single bit position is wrong.

A passing solution is synthesizable intent: no delays in the DUT, no initial blocks inside top_module, and no reference to testbench tasks. Use blocking assignments only in combinational always blocks; use non-blocking for registers clocked by clk.

Related problems

• 2-to-1 Multiplexer — Select between two 1-bit inputs using sel. When sel=0 output a; when sel=1 output b.
• 1-Bit Full Adder — Compute sum and carry-out for a + b + cin.
• 4-to-1 Multiplexer — Select one of four 1-bit inputs using a 2-bit sel. sel=00→in0, 01→in1, 10→in2, 11→in3.
• 4-to-2 Priority Encoder — Output the index of the highest-priority (MSB-most) set bit in a 4-bit input, plus a valid flag when any bit is set.

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