```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 <= 0 || width % 4 !== 0) {
    throw new Error("width must be a positive multiple of four and less than or equal to 32");
  }

  const binaryString = value.toString(2);
  const paddedBinaryString = binaryString.padStart(width, '0');

  let result = '';
  for (let i = width - 1; i >= 0; i -= 4) {
    const quadBit = paddedBinaryString.substring(i, i + 4);
    result += `${quadBit} `;
  }

  return result.trim();
}
```