Learning goals
- Distinguish decimal prefixes (KB, MB, GB) from binary prefixes (KiB, MiB, GiB)
- Convert between bits and bytes and across storage scales
- Interpret drive marketing sizes versus OS-reported capacities
Two prefix systems
SI-style data prefixes use powers of 1000: 1 KB = 1000 B, 1 MB = 1,000,000 B, 1 GB = 1,000,000,000 B. Drive makers often advertise this way.
Binary prefixes use powers of 1024: 1 KiB = 1024 B, 1 MiB = 1024² B, 1 GiB = 1024³ B. Many operating systems report free space this way (sometimes still labeling it “GB”).
Bits and bytes differ by a factor of 8: 1 byte = 8 bits. Network speeds are often in bits per second (Mbit/s), while file sizes are usually in bytes.
Decimal vs binary megabyte
1 MB = 10^6 B and 1 MiB = 2^20 B = 1,048,576 B
1 MiB is about 4.86% larger than 1 MB. At gigabyte scale the gap is larger: 1 GiB ≈ 1.074 GB.
Bits and bytes
bytes = bits ÷ 8 and bits = bytes × 8
A 100 Mbit/s link transfers 12.5 MB of payload per second in ideal conditions (100 ÷ 8), ignoring protocol overhead.
Example 1 — GB to GiB
Given
A drive is labeled 500 GB (decimal). About how many GiB is that?
Steps
- 500 GB = 500 × 10^9 = 5 × 10^11 bytes.
- Divide by 2^30 (bytes per GiB): 5×10^11 ÷ 1,073,741,824 ≈ 465.66.
Answer
About 466 GiB — close to what many OSes show for a “500 GB” drive.
Tip: The “missing” space is mostly prefix mismatch, not always a formatting loss.
Example 2 — File size MB to MiB
Given
Convert 250 MB (decimal) to MiB.
Steps
- 250 MB = 250 × 1,000,000 = 250,000,000 bytes.
- ÷ 1,048,576 ≈ 238.42 MiB.
Answer
250 MB ≈ 238.4 MiB.
Example 3 — Bits to megabytes
Given
A download is quoted as 40,000,000 bits. How many MB is that?
Steps
- Convert to bytes: 40,000,000 ÷ 8 = 5,000,000 B.
- Convert to MB: 5,000,000 ÷ 1,000,000 = 5 MB.
Answer
40,000,000 bits = 5 MB.
Assuming GB always means GiB
Common mistake
Expecting a 1 TB (10^12 B) drive to show exactly 1000 “GB” in a binary-reporting OS.
Better approach
1 TB decimal ≈ 931 GiB. Compare apples to apples: GB↔GB or GiB↔GiB.
Confusing Mbit/s with MB/s
Common mistake
Reading “100 Mbps” as 100 megabytes per second.
Better approach
Mbps is megabits per second. Divide by 8 for an upper-bound MB/s (≈12.5), then allow for overhead.
Check your understanding
1.How many bytes are in 2 KiB?
Answer: 2 × 1024 = 2048 B.
2.Convert 16 bits to bytes.
Answer: 16 ÷ 8 = 2 B.
3.Is 1 GiB larger or smaller than 1 GB?
Answer: Larger — 1 GiB ≈ 1.074 GB.
Key takeaways
- KB/MB/GB are usually 1000-based; KiB/MiB/GiB are 1024-based.
- Bits × 8 = bytes; network rates in bits look larger than byte rates.
- Drive ads and OS readouts often disagree because of prefix systems.
- Name the unit system before converting so factors stay consistent.