```ts
/** Render a value as fixed-width unsigned binary, nibble-grouped. */
export function formatBits(value: number, width: number): string {
  if (!Number.isInteger(value) || value < 0) {
    throw new Error("value must be a non-negative integer");
  }
  if (width % 4 !== 0 || width > 32) {
    throw new Error("width must be a positive multiple of four not exceeding 32");
  }
  const binary = value.toString(2).padStart(width, '0');
  if (binary.length !== width) {
    throw new Error("value does not fit in the specified width");
  }
  return binary.match(/.{1,4}/g)?.join(' ') || '';
}
```