EB to Tbit converter

What are exabytes and terabits?

Exabytes (EB) and terabits (Tbit) are units for measuring digital data. An exabyte represents an enormous volume of data—equivalent to 1 billion gigabytes. Terabits quantify data transfer speeds or bandwidth, commonly used in networking. These units belong to the International System of Units (SI), which uses base-10 (decimal) prefixes. For context:

• 1 EB = 1,000,000,000,000,000,000 bytes ($10^{18}$ bytes)
• 1 Tbit = 1,000,000,000,000 bits ($10^{12}$ bits).

In computing, a parallel system exists: the binary (IEC) standard. It uses base-2 prefixes:

• 1 exbibyte (EiB) = 1,152,921,504,606,846,976 bytes ($2^{60}$ bytes)
• 1 tebibit (Tibit) = 1,099,511,627,776 bits ($2^{40}$ bits).

The SI and IEC systems explained

SI (decimal) system:
Adopted globally for scientific and commercial use, SI prefixes increase by factors of 1,000. This system defines:

• Exabyte (EB): $10^{18}$ bytes
• Terabit (Tbit): $10^{12}$ bits.
  Hard drive manufacturers and telecom companies often use SI units for simplicity.

IEC (binary) system:
Developed in 1998 by the International Electrotechnical Commission, this system addresses computing’s binary nature. Prefixes increase by factors of 1,024 ($2^{10}$):

• Exbibyte (EiB): $2^{60}$ bytes
• Tebibit (Tibit): $2^{40}$ bits.
  Operating systems (e.g., Windows, Linux) and memory/storage software typically display data in IEC units.

Key conversion formulas

All formulas account for the byte-to-bit relationship (1 byte = 8 bits).

Within SI system:

• EB to Tbit:

Within IEC system:

• EiB to Tibit:

Cross-system conversions:

• EB to EiB:

• Tbit to Tibit:

Examples of conversions

Example 1: A data center stores 5 EB of user data. Convert to Tbit (SI):

Context: This helps network engineers design infrastructure to transfer this data at 100 Tbit/s, requiring 400 seconds.

Example 2: A supercomputer uses 2 EiB of RAM. Convert to Tibit (IEC):

Context: Memory bandwidth calculations for high-performance computing rely on such conversions.

Example 3: An internet provider offers 10 Tbit/s bandwidth. Convert to Tibit/s (cross-system):

Note: The ~9% “loss” arises from the SI/IEC discrepancy, critical for accurate service-level agreements.

Why two systems exist

• Historical context: Early computing used SI prefixes for binary quantities (e.g., 1 KB = 1,024 bytes), causing confusion. The IEC standard resolved this in 1998 by introducing distinct binary prefixes (KiB, MiB, GiB).
• Practical necessity: SI units align with physics/engineering conventions, while IEC units reflect digital hardware’s base-2 architecture (e.g., memory addressing).

Practical applications

• Cloud storage: A provider advertises 1 EB of SI-based storage. Users’ systems show ~0.867 EiB, explaining “missing” space.
• Network upgrades: Converting 100 Tbit/s (SI) to Tibit/s (IEC) ensures routers meet actual throughput demands.
• Data laws: Regulations like GDPR specify data in SI units (e.g., “exabytes of processed data”), while audits use IEC for precision.
• Scientific research: CERN’s Large Hadron Collider generates ~1 EB (SI) of data yearly, requiring IEC-based tools for analysis.

Frequently asked questions

How many Tibit are in 3 EB?

First, convert EB to Tbit (SI), then Tbit to Tibit (IEC):

Result: ~21.83 million Tibit.

Why does my OS show less storage than advertised?

A 1 TB (SI) hard drive equals $10^{12}$ bytes. In IEC:

Thus, it displays as ~0.909 TiB, not 1 TiB. This is expected, not a defect.

Are exabytes and exbibytes interchangeable?

No. 1 EB (SI) = $10^{18}$ bytes, while 1 EiB (IEC) = $2^{60}$ bytes $\approx 1.1529 \times 10^{18}$ bytes. Misuse causes significant errors in large-scale systems.

Which system should I use for networking?

Use SI (Tbit) for bandwidth (e.g., fiber-optic speeds), as telecom standards follow decimal units. Use IEC (Tibit) for data transfer between servers, where binary alignment matters.

Can I convert directly from EB to Tibit?

Yes, but it requires two steps:

1. Convert EB to bits: $\text{EB} \times 8 \times 10^{18}$
2. Convert bits to Tibit: $\text{bits} \div 2^{40}$
   Combined formula:

For 0.5 EB: $0.5 \times 7,275,957.614183426 \approx 3,637,978.81 \text{ Tibit}$.

Notes on accuracy

• Precision: Cross-system conversions involve irrational numbers (e.g., $\frac{10^{18}}{2^{60}}$). Use 10+ decimal places for critical applications.
• Standards: IEEE and ISO mandate specifying “EB” (SI) or “EiB” (IEC) in documentation to prevent ambiguity.

Historical fact

The term “exabyte” was coined in the 1970s, but the first 1 EB storage system wasn’t realized until 2008 (CERN’s LHC). The IEC binary prefixes emerged from a 1996 proposal to end the “kilo = 1,000 or 1,024?” debate.