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55. MUX Tree using Loops

Build an 8-to-1 multiplexer using a 3-level tree of 2:1 muxes. Drive each level with one bit of sel, from LSB to MSB. Implement as a tree using a single always @* with for loops (constant bounds).

Requirements

  • Module: mux8_tree
  • Inputs: d[7:0], sel[2:0]
  • Output: y

Behavior

  • Inputs: d[7:0] (eight 1-bit inputs)
  • Select: sel[2:0] (binary index 0–7)
  • Output: y = d[sel]

 

Need Help? Refer to the Quick Guide below

If-Else Statement

Syntax:

if (expression)
   statement;
else if (expression)
   statement;
else
   statement;

Key Rules

  • expression must evaluate to a 1-bit result (0, 1, x, z).
  • Execution is first true branch wins (checked top to bottom).
  • If none match and no else, no action occurs.

Common Uses

  • Combinational decision making inside always @(*).
  • Priority logic (highest branch gets priority).

Guidelines

  • Always use full coverage (else or default) to avoid unintended latch inference.
  • Use begin…end for multiple statements.
  • Use case for parallel decisions; if-else is better for priority logic.

Example

always @(*) begin
  if (sel == 2'b00)     y = a;
  else if (sel == 2'b01) y = b;
  else if (sel == 2'b10) y = c;
  else                   y = d; // avoids latch
end

Case, Casez, Casex Statements

General Syntax:

case (expression)
   value1: statement;
   value2: statement;
   ...
   default: statement;
endcase

Case

  • Exact match (bit-by-bit, including x/z).
  • Good for one-hot encoding or multi-way decode.

Casez

  • Treats Z and ? as don’t-cares.
  • Useful for partial matches and encoders.
casez (opcode)
   4'b1???: alu_op = ADD;
   4'b01??: alu_op = SUB;
   default: alu_op = NOP;
endcase

Casex

  • Treats X, Z, and ? as don’t-cares.
  • Risky → can mask real unknowns in simulation.
  • Synthesis tools may treat it differently; use sparingly.

Guidelines

  • Always include default to prevent latches.
  • casez is preferred over casex in synthesizable RTL.
  • Case statements are parallel (not priority) unless overlapping values are used.

For Loop Statement

Syntax:

for (init; condition; step) statement;

Rules

  • All loop control variables must be declared (integer i;).
  • Loop unrolls during elaboration if bounds are static.
  • Synthesizable only with constant bounds.

Example

integer i;
always @(*) begin
  sum = 0;
  for (i=0; i<8; i=i+1) begin
    sum = sum + data[i];
  end
end

Guidelines

  • Use for loops to describe repeated hardware structures (not like software loops).
  • Avoid unbounded or runtime-dependent loops in RTL → not synthesizable.
  • For simulation-only, forever and while are also allowed.