```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 || width > 32) {
    throw new Error("width must be a positive multiple of four and less than or equal to 32");
  }

  const binaryString = value.toString(2);
  const paddingLength = Math.max(0, width - binaryString.length);

  let result = '0'.repeat(paddingLength) + binaryString;

  // Split into groups of four bits
  return result.match(/.{4}/g)?.join(' ') || '';
}
```