```ts
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, up to 32 bits.");
  }

  const binary = value.toString(2).padStart(width, '0');
  const groups = [];
  
  for (let i = 0; i < binary.length; i += 4) {
    groups.push(binary.substring(i, i + 4));
  }
  
  return groups.join(' ');
}
```