diff --git a/amaranth/_utils.py b/amaranth/_utils.py
index 886de59..35adcf9 100644
--- a/amaranth/_utils.py
+++ b/amaranth/_utils.py
@@ -2,15 +2,27 @@ import contextlib
 import functools
 import warnings
 import linecache
+import operator
 import re
 from collections import OrderedDict
 from collections.abc import Iterable
 
 
-__all__ = ["flatten", "union", "final", "deprecated", "get_linter_options",
+__all__ = ["to_binary", "flatten", "union", "final", "deprecated", "get_linter_options",
            "get_linter_option"]
 
 
+def to_binary(n: int, width: int) -> str:
+    """Formats ``n`` as exactly ``width`` binary digits, including when ``width`` is 0"""
+    n = operator.index(n)
+    width = operator.index(width)
+    if n not in range(1 << width):
+        raise ValueError(f"{n} does not fit in {width} bits")
+    if width == 0:
+        return ""
+    return f"{n:0{width}b}"
+
+
 def flatten(i):
     for e in i:
         if isinstance(e, str) or not isinstance(e, Iterable):
diff --git a/amaranth/hdl/_ast.py b/amaranth/hdl/_ast.py
index cd2b500..3b71bc1 100644
--- a/amaranth/hdl/_ast.py
+++ b/amaranth/hdl/_ast.py
@@ -2768,15 +2768,9 @@ class Switch(Statement):
                 if isinstance(key, str):
                     key = "".join(key.split()) # remove whitespace
                 elif isinstance(key, int):
-                    key = format(key & key_mask, "b").rjust(len(self.test), "0")
-                    # fixup for 0-width test
-                    if key_mask == 0:
-                        key = ""
+                    key = to_binary(key & key_mask, len(self.test))
                 elif isinstance(key, Enum):
-                    key = format(key.value & key_mask, "b").rjust(len(self.test), "0")
-                    # fixup for 0-width test
-                    if key_mask == 0:
-                        key = ""
+                    key = to_binary(key.value & key_mask, len(self.test))
                 else:
                     raise TypeError("Object {!r} cannot be used as a switch key"
                                     .format(key))
diff --git a/amaranth/hdl/_ir.py b/amaranth/hdl/_ir.py
index 04c1d9c..10b9ab7 100644
--- a/amaranth/hdl/_ir.py
+++ b/amaranth/hdl/_ir.py
@@ -3,7 +3,7 @@ from collections import defaultdict, OrderedDict
 import enum
 import warnings
 
-from .._utils import flatten
+from .._utils import flatten, to_binary
 from .. import tracer, _unused
 from . import _ast, _cd, _ir, _nir
 
@@ -880,7 +880,7 @@ class NetlistEmitter:
             conds = []
             for case_index in range(len(elems)):
                 cell = _nir.Matches(module_idx, value=index,
-                                       patterns=(f"{case_index:0{len(index)}b}",),
+                                       patterns=(to_binary(case_index, len(index)),),
                                        src_loc=value.src_loc)
                 subcond, = self.netlist.add_value_cell(1, cell)
                 conds.append(subcond)
@@ -985,7 +985,7 @@ class NetlistEmitter:
             conds = []
             for case_index in range(num_cases):
                 cell = _nir.Matches(module_idx, value=offset,
-                                    patterns=(f"{case_index:0{len(offset)}b}",),
+                                    patterns=(to_binary(case_index, len(offset)),),
                                     src_loc=lhs.src_loc)
                 subcond, = self.netlist.add_value_cell(1, cell)
                 conds.append(subcond)
@@ -1006,7 +1006,7 @@ class NetlistEmitter:
             conds = []
             for case_index in range(len(lhs.elems)):
                 cell = _nir.Matches(module_idx, value=index,
-                                       patterns=(f"{case_index:0{len(index)}b}",),
+                                       patterns=(to_binary(case_index, len(index)),),
                                        src_loc=lhs.src_loc)
                 subcond, = self.netlist.add_value_cell(1, cell)
                 conds.append(subcond)