diff --git a/src/Convert/UnbasedUnsized.hs b/src/Convert/UnbasedUnsized.hs
index 6734b82..1eec4d8 100644
--- a/src/Convert/UnbasedUnsized.hs
+++ b/src/Convert/UnbasedUnsized.hs
@@ -3,9 +3,9 @@
  -
  - Conversion for unbased, unsized literals ('0, '1, 'z, 'x)
  -
- - Maintaining the unsized-ness of the literals is critical, but those digits
- - are all equivalent regardless of base. We simply convert them to all use a
- - binary base for compatibility with Verilog-2005.
+ - We convert the literals to be signed to enable sign extension, and give them
+ - a size of 1 and a binary base. These values implicitly cast as desired in
+ - Verilog-2005.
  -}
 
 module Convert.UnbasedUnsized (convert) where
@@ -25,6 +25,6 @@ digits = ['0', '1', 'x', 'z', 'X', 'Z']
 convertExpr :: Expr -> Expr
 convertExpr (Number ['\'', ch]) =
     if elem ch digits
-        then Number ("'b" ++ [ch])
+        then Number ("1'sb" ++ [ch])
         else error $ "unexpected unbased-unsized digit: " ++ [ch]
 convertExpr other = other
diff --git a/test/basic/cast.v b/test/basic/cast.v
index a658614..6834033 100644
--- a/test/basic/cast.v
+++ b/test/basic/cast.v
@@ -21,7 +21,7 @@ module top;
         $display("%b %b", y, {8'b0, y});
         $display("%b %b", z, {35'b0, z});
     end
-    localparam foo = 0;
+    localparam [0:0] foo = 0;
     localparam [31:0] bar = 32'b0;
     initial $display("%b %b", foo, bar);
 endmodule
diff --git a/test/basic/dimensions.v b/test/basic/dimensions.v
index fea0c15..ef8e8eb 100644
--- a/test/basic/dimensions.v
+++ b/test/basic/dimensions.v
@@ -15,42 +15,42 @@ module top;
         $display(1);
         $display(160);
 
-        $display(16, 16, 'bx);
-        $display(16, 16, 'bx);
-        $display(1, 1, 'bx);
-        $display(16, 16, 'bx);
-        $display(1, 1, 'bx);
-        $display(1, 1, 'bx);
+        $display(16, 16, 1'bx);
+        $display(16, 16, 1'bx);
+        $display(1, 1, 1'bx);
+        $display(16, 16, 1'bx);
+        $display(1, 1, 1'bx);
+        $display(1, 1, 1'bx);
         $display(1);
         $display(0);
         $display(16);
 
-        $display(32, 32, 'bx);
-        $display(31, 31, 'bx);
-        $display(0, 0, 'bx);
-        $display(31, 31, 'bx);
-        $display(0, 0, 'bx);
-        $display(1, 1, 'bx);
+        $display(32, 32, 1'bx);
+        $display(31, 31, 1'bx);
+        $display(0, 0, 1'bx);
+        $display(31, 31, 1'bx);
+        $display(0, 0, 1'bx);
+        $display(1, 1, 1'bx);
         $display(1);
         $display(0);
         $display(32);
 
-        $display('bx, 'bx, 'bx);
-        $display('bx, 'bx, 'bx);
-        $display('bx, 'bx, 'bx);
-        $display('bx, 'bx, 'bx);
-        $display('bx, 'bx, 'bx);
-        $display('bx, 'bx, 'bx);
+        $display(1'bx, 1'bx, 1'bx);
+        $display(1'bx, 1'bx, 1'bx);
+        $display(1'bx, 1'bx, 1'bx);
+        $display(1'bx, 1'bx, 1'bx);
+        $display(1'bx, 1'bx, 1'bx);
+        $display(1'bx, 1'bx, 1'bx);
         $display(0);
         $display(0);
         $display(1);
 
-        $display(8, 8, 'bx);
-        $display(7, 7, 'bx);
-        $display(0, 0, 'bx);
-        $display(7, 7, 'bx);
-        $display(0, 0, 'bx);
-        $display(1, 1, 'bx);
+        $display(8, 8, 1'bx);
+        $display(7, 7, 1'bx);
+        $display(0, 0, 1'bx);
+        $display(7, 7, 1'bx);
+        $display(0, 0, 1'bx);
+        $display(1, 1, 1'bx);
         $display(1);
         $display(0);
         $display(8);
diff --git a/test/basic/unbased_unsized.sv b/test/basic/unbased_unsized.sv
new file mode 100644
index 0000000..cb86473
--- /dev/null
+++ b/test/basic/unbased_unsized.sv
@@ -0,0 +1,10 @@
+`define TEST(value) \
+    logic [63:0] val_``value = 'value; \
+    initial $display(`"'value -> %b %b", val_``value, 'value);
+
+module top;
+    `TEST(1);
+    `TEST(0);
+    `TEST(x);
+    `TEST(z);
+endmodule
diff --git a/test/basic/unbased_unsized.v b/test/basic/unbased_unsized.v
new file mode 100644
index 0000000..1763368
--- /dev/null
+++ b/test/basic/unbased_unsized.v
@@ -0,0 +1,10 @@
+`define TEST(value) \
+    wire [63:0] val_``value = {64{1'b``value}}; \
+    initial $display(`"'value -> %b %b", val_``value, 1'b``value);
+
+module top;
+    `TEST(1)
+    `TEST(0)
+    `TEST(x)
+    `TEST(z)
+endmodule