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diff --git a/rtl/simple_alu.sv b/rtl/simple_alu.sv
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+// Simple 32-bit ALU supporting addition and subtraction (sel=0/1).
+// Outputs are registered. Overflow/underflow detected via 33-bit extended arithmetic.
+// Active-low synchronous reset. Used as a sandbox for formal verification.
+module simple_alu (
+
+    //inputs
+    input logic        clk_i,
+    input logic [31:0] a_i,
+    input logic [31:0] b_i,
+    input logic        sel_i,         //sel = 0 -> ADD, sel = 1 -> SUB
+    input logic        rst_ni,        //active LOW sync reset
+
+    //outputs
+    output logic [31:0] y_o,
+    output logic        overflow_o
+);
+
+    logic [32:0] sum;
+    logic [32:0] diff;
+    logic [31:0] y_r;
+    logic        overflow_r;
+    logic [31:0] y_next;
+    logic        overflow_next;
+
+    always_comb begin
+        sum  = {1'b0, a_i} + {1'b0, b_i};
+        diff = {1'b0, a_i} - {1'b0, b_i};
+
+        y_next        = '0;
+        overflow_next = '0;
+
+        if (rst_ni) begin
+            case (sel_i)
+                0: begin
+                    y_next        = sum[31:0];
+                    overflow_next = sum[32];
+                end
+                1: begin
+                    y_next        = diff[31:0];
+                    overflow_next = diff[32];
+                end
+                default: begin
+                    y_next        = '0;
+                    overflow_next = '0;
+                end
+            endcase
+        end
+    end
+
+    always_ff @(posedge clk_i) begin
+        y_r        <= y_next;
+        overflow_r <= overflow_next;
+    end
+
+    assign y_o        = y_r;
+    assign overflow_o = overflow_r;
+
+endmodule