Data Storage Converter

Decimal vs. Binary: The Source of Most Confusion

Data storage units have two competing definitions, and the difference matters when your "1 TB" hard drive shows up as 931 GB in Windows. The confusion comes from the prefix "kilo." In the metric system, kilo always means 1,000. But early computer engineers found it convenient to use 1,024 (which is 2¹⁰) because computers work in powers of two. and 1,024 is close enough to 1,000 that they used the same prefixes.

To resolve this, the IEEE and IEC introduced binary prefixes: kibibyte (KiB) = 1,024 bytes, mebibyte (MiB) = 1,048,576 bytes, gibibyte (GiB) = 1,073,741,824 bytes. Hard drive manufacturers use decimal (1 GB = 1,000,000,000 bytes), while operating systems traditionally report in binary (1 GB displayed = 1,073,741,824 bytes). A 1 TB drive sold as 1,000,000,000,000 bytes = 931.32 GiB. which is why it appears smaller than advertised.

Key Conversion Factors

Using decimal (SI) definitions:

• 1 byte = 8 bits
• 1 kilobyte (KB) = 1,000 bytes
• 1 megabyte (MB) = 1,000,000 bytes
• 1 gigabyte (GB) = 1,000,000,000 bytes
• 1 terabyte (TB) = 1,000,000,000,000 bytes
• 1 petabyte (PB) = 1,000,000,000,000,000 bytes

Example: a 25 MB email attachment is 25 × 8 = 200 megabits. If your internet connection speed is 100 Mbps (megabits per second), that file downloads in 200 ÷ 100 = 2 seconds. assuming no overhead.

Bits vs. Bytes in Networking

Internet speeds are always quoted in bits per second (Mbps, Gbps), while file sizes are quoted in bytes (MB, GB). This catches many people out. A 500 Mbps connection transfers 500 ÷ 8 = 62.5 megabytes per second. When you see a download speed in your browser showing "MB/s," multiply by 8 to compare it to your advertised plan speed in Mbps.

Source: IEEE 1541-2002. Prefixes for Binary Multiples