Binary prefixes

Just like we have decimal prefixes, such as mega (for x1,000,000) and nano (for x0.000001), we also have binary prefixes, which are based on powers of 2.

Common binary prefixes

An interesting pattern here is that each prefix is 1024 times larger than the previous one, since 2^{10} = 1024.

Example conversions

Example: Convert 4 kibibytes to bytes.

• 1 kibibyte (KiB) = 2^{10} bytes (B)
• 4 KiB = 4 \times 2^{10} B = 4096 B
• Answer: 4096 bytes

Example: Convert 3 mebibytes to bytes.

• 1 mebibyte (MiB) = 2^{20} bytes (B)
• 3 MiB = 3 \times 2^{20} B = 3,145,728 B
• Answer: 3,145,728 bytes

Example: Convert 2 gibibytes to mebibytes.

• 1 gibibyte (GiB) = 2^{30} bytes (B)
• 1 mebibyte (MiB) = 2^{20} bytes (B)
• Therefore, 1 GiB = 2^{30} \div 2^{20} = 2^{10} MiB = 1024 MiB
• 2 GiB = 2 \times 1024 MiB = 2048 MiB
• Answer: 2048 mebibytes

Example: Convert 5 tebibytes to gibibytes.

• 1 tebibyte (TiB) = 2^{40} bytes (B)
• 1 gibibyte (GiB) = 2^{30} bytes (B)
• Therefore, 1 TiB = 2^{40} \div 2^{30} = 2^{10} GiB = 1024 GiB
• 5 TiB = 5 \times 1024 GiB = 5120 GiB
• Answer: 5120 gibibytes

Example: Convert 1 pebibyte to gibibytes.

• 1 pebibyte (PiB) = 2^{50} bytes (B)
• 1 gibibyte (GiB) = 2^{30} bytes (B)
• Therefore, 1 PiB = 2^{50} \div 2^{30} = 2^{20} GiB = 1,048,576 GiB
• 1 PiB = 1,048,576 GiB
• Answer: 1,048,576 gibibytes

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