Data size converter

What is a data size converter?

A digital data converter is a tool for converting values between different units of digital information, such as bits, bytes, kilobytes, megabytes, and others. It accounts for two main numeral systems: decimal (SI) and binary (IEC), which is crucial for accurate calculations in IT, telecommunications, and data storage.

One key purpose of the converter is to eliminate confusion between systems. For example:

• 1 kilobyte (KB) in the decimal system equals 1,000 bytes,
• 1 kibibyte (KiB) in the binary system equals 1,024 bytes.
  The difference becomes significant when working with gigabytes and terabytes.

This converter supports convertations between units like:
bit, nibble (4 bits or half a byte), byte (B), kilobit (kbit), kilobyte (KB), megabit (Mbit), megabyte (MB), gigabit (Gbit), gigabyte (GB), terabit (Tbit), terabyte (TB), petabit (Pbit), petabyte (PB), exabit (Ebit), exabyte (EB), zettabit (Zbit), zettabyte (ZB), yottabit (Ybit), yottabyte (YB), kibibit (Kibit), kibibyte (KiB), mebibit (Mibit), mebibyte (MiB), gibibit (Gibit), gibibyte (GiB), tebibit (Tibit), tebibyte (TiB), pebibit (Pibit), pebibyte (PiB), exbibit (Eibit), exbibyte (EiB), zebibit (Zibit), zebibyte (ZiB), yobibit (Yibit), yobibyte (YiB).

Binary (IEC) vs. Decimal (SI) Systems: Key Differences

Base units

• Bit (b): Smallest unit of information, representing 0 or 1.
• Byte (B): Composed of 8 bits.

Decimal system (SI)

Based on powers of 10, where each step is $10^3$:

• Kilobyte (KB): $10^3 = 1,000$ bytes.
• Megabyte (MB): $10^6 = 1,000,000$ bytes.
• Gigabyte (GB): $10^9 = 1,000,000,000$ bytes.
• Terabyte (TB): $10^{12} = 1,000,000,000,000$ bytes.
• Petabyte (PB): $10^{15}$ bytes.
• Exabyte (EB): $10^{18}$ bytes.
• Zettabyte (ZB): $10^{21}$ bytes.
• Yottabyte (YB): $10^{24}$ bytes.

Used by:

• HDD/SSD manufacturers,
• Internet speed measurements (e.g., 100 Mbps).

Binary system (IEC)

Based on powers of 2, where each step is $2^{10} = 1,024$:

• Kibibyte (KiB): $2^{10} = 1,024$ bytes.
• Mebibyte (MiB): $2^{20} = 1,048,576$ bytes.
• Gibibyte (GiB): $2^{30}$ bytes.
• Tebibyte (TiB): $2^{40}$ bytes.
• Pebibyte (PiB): $2^{50}$ bytes.
• Exbibyte (EiB): $2^{60}$ bytes.
• Zebibyte (ZiB): $2^{70}$ bytes.
• Yobibyte (YiB): $2^{80}$ bytes.

Used by:

• Operating systems (e.g., Windows displays file sizes in GiB but labels them “GB”),
• Software development and programming.

Conversion formulas

1. Converting between bits and bytes

System-agnostic:

Example:
$16\ \text{bits} = \frac{16}{8} = 2\ \text{B}$.

2. Converting between data units

Formula depends on the system:

• Decimal (SI):

• Binary (IEC):

Where:
$n$ is the difference in unit orders (e.g., KB to MB: $n = 3$, since $1\ \text{MB} = 10^3\ \text{KB}$).

Calculation examples

Example 1: Convert 500 GB to TB (SI Standard)

Example 2: Convert 500 GiB to TiB (IEC Standard)

Example 3: Convert 100 Mbit to MB

Notes:

• Internet speed conversion: $50\ \text{Mbps} \div 8 = 6.25\ \text{MB/s}$.
• KB vs. KiB: $1\ \text{KB} = 1,000\ \text{B}, \quad 1\ \text{KiB} = 1,024\ \text{B}$.
• Bits vs. bytes: 16 Mbps ≠ 16 MB/s. Divide by 8 to get bytes.
• For gamers: A 80 GB game on Steam will occupy ~74.5 GiB on disk.

Frequently Asked Questions

How to convert 250 MB to gigabytes (SI)?

How many bits are in 5 MiB (IEC)?