EB to Gbit converter

What is an exabyte and gigabit?

An exabyte (EB) is a unit of digital information equal to $10^{18}$ bytes in the International System of Units (SI). It represents one quintillion bytes, commonly used to quantify massive data volumes like global internet traffic or cloud storage. A gigabit (Gbit) is another SI unit representing $10^9$ bits, frequently used for network bandwidth (e.g., 1 Gbit/s internet speed). Crucially, 1 byte = 8 bits, so unit conversions require scaling by 8.

In contrast, the binary system (IEC 80000-13 standard) uses base-2 units:

• Exbibyte (EiB): $2^{60}$ bytes = 1,152,921,504,606,846,976 bytes.
• Gibibit (Gibit): $2^{30}$ bits = 1,073,741,824 bits.

These systems coexist due to computing’s binary nature (IEC) versus SI’s decimal simplicity.

The SI (decimal) and binary (IEC) systems

SI system (base-10)

Developed for scientific uniformity, SI prefixes like giga- ($10^9$) and exa- ($10^{18}$) use powers of 10. Common in storage marketing (hard drives, SSDs) and telecommunications.

• Units: EB (exabyte), Gbit (gigabit).
• Key trait: Aligns with the metric system, simplifying large-scale calculations.

Binary system (base-2, IEC standard)

Created in 1998 to resolve computing’s inherent binary structure. Prefixes like gibi- (Gi, $2^{30}$) and exbi- (Ei, $2^{60}$) use powers of 2. Dominates operating systems (e.g., RAM allocation).

• Units: EiB (exbibyte), Gibit (gibibit).
• Key trait: Precisely matches memory addressing (e.g., $2^{10}$ = 1,024).

Why two systems?

Early computing borrowed SI prefixes for binary quantities (e.g., “1 KB” = 1,024 bytes). This caused confusion, prompting IEC standardization. Today:

• SI units: Storage manufacturers, network providers.
• IEC units: Software (Windows, Linux), memory design.

Conversion formulas

SI system: EB to Gbit

$\text{Gbit} = \text{EB} \times (8 \times 10^{9})$
Derivation:
1 EB = $10^{18}$ bytes = $8 \times 10^{18}$ bits.
1 Gbit = $10^9$ bits.
Thus:
$\text{Gbit} = \frac{\text{EB} \times 8 \times 10^{18}}{10^9} = \text{EB} \times 8 \times 10^{9}$

IEC system: EiB to Gibit

$\text{Gibit} = \text{EiB} \times (8 \times 2^{30})$
Derivation:
1 EiB = $2^{60}$ bytes = $8 \times 2^{60}$ bits.
1 Gibit = $2^{30}$ bits.
Thus:
$\text{Gibit} = \frac{\text{EiB} \times 8 \times 2^{60}}{2^{30}} = \text{EiB} \times 8 \times 2^{30}$

Critical notes

• Never mix systems: Convert within SI or IEC only.
• Bits vs. bytes: Multiply by 8 when converting bytes→bits.
• Precision: Use exact values ($2^{30} = 1,073,741,824$) for accuracy.

Step-by-step examples

Example 1: SI conversion (EB to Gbit)

Convert 3 EB to Gbit:
$\text{Gbit} = 3 \times 8 \times 10^{9} = 24,000,000,000 \text{ Gbit}$
Real-world context: 3 EB could represent ~60 billion HD movies. At 24 Tbit/s (global internet capacity), transmitting this would take ~11.6 days.

Example 2: IEC conversion (EiB to Gibit)

Convert 0.5 EiB to Gibit:
First, calculate $8 \times 2^{30}$:
$8 \times 1,073,741,824 = 8,589,934,592$
Then:
$\text{Gibit} = 0.5 \times 8,589,934,592 = 4,294,967,296 \text{ Gibit}$
Real-world context: 0.5 EiB equals ~580,000 high-end smartphones (128 GB each).

Example 3: Cross-unit verification

Verify 1 EB vs. 1 EiB:

• 1 EB = $8 \times 10^{18}$ bits.
• 1 EiB = $8 \times 2^{60}$ bits ≈ $9.223 \times 10^{18}$ bits.
  Thus, 1 EiB ≈ 1.1529 EB. This 15.29% difference explains why a 1 EB drive shows as ~0.867 EiB in binary systems.

Practical applications

Data center scaling

A cloud provider stores 50 EB of user data. To design a network transferring backups at 100 Gbit/s:

1. Convert storage to Gbit:
   $50 \text{ EB} \times 8 \times 10^{9} = 400,000,000,000 \text{ Gbit}$
2. Transfer time:
   $\frac{400,000,000,000 \text{ Gbit}}{100 \text{ Gbit/s}} = 4,000,000,000 \text{ seconds} ≈ 126.8 \text{ years}$
   Solution: Parallel connections or compression are essential.

Bandwidth requirements

A video platform streams 5 EiB monthly. For 4K streams (25 Mbit/s average):

1. Convert EiB to Gibit:
   $5 \times 8 \times 2^{30} = 42,949,672,960 \text{ Gibit}$
2. Convert to Mbit (1 Gibit = 1,073.741824 Mbit):
   $42,949,672,960 \times 1,073.741824 ≈ 46,116,860,000,000 \text{ Mbit}$
3. Bandwidth needed:
   $\frac{46,116,860,000,000 \text{ Mbit}}{2,592,000 \text{ seconds/month}} ≈ 17.8 \text{ Tbit/s}$

Historical context

The term “byte” (8 bits) was coined by Werner Buchholz in 1956. SI prefixes (e.g., giga-) were standardized in 1960, but binary usage caused discrepancies. By 1998, the IEC introduced kibi, mebi, gibi to end confusion. Notably, a 1996 lawsuit against storage manufacturers highlighted the issue—customers received 93% of advertised space due to binary interpretation.

Frequently asked questions

How to convert 10 exabytes to gigabits?

Multiply by $8 \times 10^9$:
$10 \text{ EB} \times 8 \times 10^9 = 80,000,000,000 \text{ Gbit}$

Why is my 1 EB drive showing less capacity in gibibits?

Storage marketers use SI units (1 EB = $10^{18}$ bytes), but OSes use IEC (1 EiB = $2^{60}$ bytes ≈ $1.1529 \times 10^{18}$ bytes). Thus:
$1 \text{ EB} = \frac{10^{18}}{2^{60}} ≈ 0.867 \text{ EiB}$

What is bigger: 1 exbibyte or 1 exabyte?

1 EiB is larger:
$1 \text{ EiB} = 2^{60} \text{ bytes} = 1,152,921,504,606,846,976 \text{ bytes}$
$1 \text{ EB} = 10^{18} \text{ bytes} = 1,000,000,000,000,000,000 \text{ bytes}$
Difference: ~153 million GB.

Can I convert exbibytes directly to gigabits?

No—units belong to different systems. First convert EiB to Gibit (IEC), or convert EiB to EB (SI) then to Gbit. For accuracy:

1. Convert EiB → bits: Multiply by $8 \times 2^{60}$.
2. Convert bits → Gbit: Divide by $10^9$.

How many gibibits are in 0.2 exbibytes?

Use $8 \times 2^{30}$:
$0.2 \times 8 \times 1,073,741,824 = 1,717,986,918.4 \text{ Gibit}$

Is gigabit the same as gigabyte?

No. Gigabit (Gbit) measures data transfer (e.g., internet speed), while gigabyte (GB) measures storage.
$1 \text{ GB} = 8 \text{ Gbit}$
For example, downloading a 1 GB file at 1 Gbit/s takes 8 seconds.