EB to Ybit converter

Understanding data storage units: from exabytes to yottabits

Data storage measurement exists in two distinct systems: the international system of units (SI) using base-10 prefixes and the international electrotechnical commission (IEC) standard using base-2 prefixes. The SI system defines:

• Exabyte (EB) = $10^{18}$ bytes
• Yottabit (Ybit) = $10^{24}$ bits

The IEC binary system defines:

• Exbibyte (EiB) = $2^{60}$ bytes
• Yobibit (Yibit) = $2^{80}$ bits

Confusion arises because operating systems often report storage in SI units while actually using binary addressing. For example, a drive marketed as “1 TB” (1 trillion bytes) appears as ~931 GiB in Windows.

Conversion formulas

Within SI system (decimal)

$\text{Yottabits (Ybit)} = \frac{\text{Exabytes (EB)} \times 8}{10^{6}}$ Explanation: Multiply EB by 8 to convert bytes→bits, then divide by $10^6$ since 1 yottabit = $10^{24}$ bits and 1 exabyte = $10^{18}$ bytes ($10^{24}/10^{18} = 10^6$).

Within IEC system (binary)

$\text{Yobibits (Yibit)} = \frac{\text{Exbibytes (EiB)} \times 8}{2^{20}}$ Explanation: Multiply EiB by 8 for bytes→bits, then divide by $2^{20}$ because 1 yobibit = $2^{80}$ bits and 1 exbibyte = $2^{60}$ bytes ($2^{80}/2^{60} = 2^{20}$).

Cross-system conversions

$\text{EB to EiB} = \text{EB} \times \frac{10^{18}}{2^{60}}$ $\text{Ybit to Yibit} = \text{Ybit} \times \frac{10^{24}}{2^{80}}$

Step-by-step calculation examples

Example 1: Convert 3 exabytes (EB) to yottabits (Ybit) using SI units $\text{Ybit} = \frac{3 \text{ EB} \times 8}{1,000,000} = \frac{24}{1,000,000} = 0.000024 \text{ Ybit}$

Example 2: Convert 5 exbibytes (EiB) to yobibits (Yibit) using IEC units $\text{Yibit} = \frac{5 \text{ EiB} \times 8}{1,048,576} = \frac{40}{1,048,576} \approx 0.000038147 \text{ Yibit}$

Example 3: Compare 10 EB (SI) and 10 EiB (IEC) in yottabits

• 10 EB to Ybit: $\frac{10 \times 8}{1,000,000} = 0.00008 \text{ Ybit}$
• 10 EiB to Ybit: First convert EiB→EB: $10 \times \frac{2^{60}}{10^{18}} \approx 11.52 \text{ EB}$, then to Ybit: $\frac{11.52 \times 8}{1,000,000} = 0.00009216 \text{ Ybit}$

Practical applications

1. Data center scaling: A 100 EB storage array (SI) requires $100 \times 10^{18} \div 8 = 1.25 \times 10^{19}$ bits. In yottabits: $1.25 \times 10^{19} \div 10^{24} = 0.0000125 \text{ Ybit}$.

2. Global internet traffic: Annual traffic is ~3.5 ZB (zettabytes, $10^{21}$ bytes). To express in yottabits: $\frac{3.5 \times 8 \times 10^{21}}{10^{24}} = 0.028 \text{ Ybit/year}$

3. IEC in memory manufacturing: A 128 EiB RAM module contains: $\frac{128 \times 2^{60} \times 8}{2^{80}} = \frac{128 \times 8}{1,048,576} = 0.0009765625 \text{ Yibit}$

Historical context

The IEC introduced binary prefixes in 1998 to resolve ambiguity. Before this, “exabyte” ambiguously meant either $10^{18}$ bytes or $2^{60}$ bytes—a 15.3% difference. This caused legal disputes, such as in 2003 when consumers sued hard drive manufacturers over capacity discrepancies.

Technical considerations

• Accuracy: SI conversions are exact; IEC involve powers of 2.
• Storage media: SSDs/NAND flash typically use SI units, RAM uses IEC.
• Network vs. storage: Network bandwidth (e.g., 100 Gbit/s) uses bits, storage capacity uses bytes.

Frequently asked questions

What’s the difference between Ybit and Yibit?

Yottabit (Ybit) is $10^{24}$ bits (SI), while yobibit (Yibit) is $2^{80}$ bits (IEC). 1 Yibit ≈ 1.2089 Ybit—a 20.89% difference.

How to convert 25 EB to EiB?

$\text{EiB} = 25 \text{ EB} \times \frac{10^{18}}{2^{60}} = 25 \times \frac{1,000,000,000,000,000,000}{1,152,921,504,606,846,976} \approx 21.684 \text{ EiB}$

Why do operating systems show less storage than advertised?

A “1 TB” drive uses SI units ($10^{12}$ bytes), but OSes display in IEC units: $10^{12} \div 2^{40} \approx 0.9095 \text{ TiB}$.

Is internet bandwidth measured in SI or IEC units?

Bandwidth (e.g., 10 Gbit/s) universally uses SI units. 1 Gbit/s always means $10^9$ bits per second.

How many EiB equal one Yibit?

1 Yibit = $2^{80}$ bits = $2^{80} \div 8$ bytes = $2^{77}$ bytes. Since 1 EiB = $2^{60}$ bytes: $\text{EiB} = \frac{2^{77}}{2^{60}} = 2^{17} = 131,072 \text{ EiB}$

Common mistakes to avoid

• Using SI prefixes for memory (e.g., “512 GB RAM” should be “512 GiB”)
• Confusing bits (transmission) with bytes (storage)
• Assuming $10^3 = 2^{10}$ (1,000 vs 1,024) at exascale—the gap compounds exponentially.