Free disk space can be kept track of using a free list or a bit map. Disk addresses require D bits. For a disk with B blocks, of which F are free, state the condition under which the free list uses less space than the bit map.

GATE 1998 · Operating System · Disk · medium

Answer: The free list uses less space than the bitmap when F < B/D, i.e. when the number of free blocks is less than B/D.

1. Space used by the bitmap: The bitmap allocates one bit per block regardless of occupancy, so it always uses exactly B bits.
2. Space used by the free list: The free list stores one D-bit address for each of the F free blocks, so total = F * D bits.
3. Derive the condition: We need Space_freelist < Space_bitmap, i.e. F*D < B. Dividing both sides by D gives F < B/D.