GB to Pbit converter

What are Gigabytes (GB) and Petabits (Pbit)?

In digital data measurement, units like gigabyte (GB) and petabit (Pbit) belong to two distinct systems:

1. Base-10 (SI System): Follows the International System of Units, where prefixes like giga- and peta- denote powers of 10.

   • 1 gigabyte (GB) = $10^9$ bytes = 1,000,000,000 bytes.
   • 1 petabit (Pbit) = $10^{15}$ bits = 1,000,000,000,000,000 bits.

2. Binary System (IEC Standard): Uses base-2, where prefixes like gibi- and pebi- denote powers of 2.

   • 1 gibibyte (GiB) = $2^{30}$ bytes = 1,073,741,824 bytes.
   • 1 pebibit (Pibit) = $2^{50}$ bits = 1,125,899,906,842,624 bits.

Confusion arises because operating systems and storage manufacturers often use GB to represent GiB, leading to discrepancies in reported data sizes.

Formula for conversions

Base-10 (SI) conversions

• Gigabytes to Petabits:

Explanation: Since 1 byte = 8 bits and 1 Pbit = $10^{15}$ bits, we divide by $\frac{10^{15}}{(8 \times 10^9)}$ = $10^{-6} \times 8$.

• Petabits to Gigabytes:

Binary (IEC) conversions

• Gibibytes to Pebibits:

Explanation: 1 GiB = $2^{30}$ bytes = $8 \times 2^{30}$ bits. To convert to Pibit ($2^{50}$ bits), divide by $\frac{2^{50}}{(8 \times 2^{30})}$ = $8 \times 2^{-20}$.

• Pebibits to Gibibytes:

Examples

Example 1: Converting 500 GB to Petabits (SI)

Application: A 500 GB SSD stores 0.004 Pbit of data.

Example 2: Converting 1024 GiB to Pebibits (IEC)

Application: A 1024 GiB RAM module holds 0.0078 Pibit.

Example 3: Converting 1.5 TB to both systems

• SI units:
  $1.5\, \text{TB} = 1500\, \text{GB}$ $$1500\, \text{GB} \times 8 \times 10^{-6} = 0.012\, \text{Pbit}$$
• IEC units:
  $1.5\, \text{TiB} = 1536\, \text{GiB}$ $$1536\, \text{GiB} \times 8 \times 2^{-20} = 0.01171875\, \text{Pibit}$$

Note: The difference between 0.012 Pbit (SI) and 0.0117 Pibit (IEC) highlights the impact of unit systems.

Notes

1. Unit labels matter: Always confirm whether values follow SI (base-10) or IEC (base-2).
2. Storage vs. transmission: Storage devices (e.g., HDDs) often use IEC units but label them as SI (e.g., “GB” instead of “GiB”). Network bandwidth typically uses SI units.
3. Precision in computing: RAM and operating systems frequently use binary units, while data transfer rates use decimal units.

Frequently asked questions

How many petabits are in 10,000 gigabytes?

Using the SI formula:

Answer: 10,000 GB equals 0.08 Pbit.

What is the difference between Pbit and Pibit?

• Pbit (Petabit): $10^{15}$ bits (SI).
• Pibit (Pebibit): $2^{50}$ bits (IEC).
  Example: 1 Pibit ≈ 1.1259 Pbit, making it ~12.59% larger.

Why do two unit systems exist?

The SI system simplifies decimal-based calculations (e.g., network speeds). The IEC standard addresses binary-based computing (e.g., memory chips), reducing ambiguity.

How to convert 5 Pibit to Gibibytes?

Using the IEC formula:

Answer: 5 Pibit equals 655,360 GiB.

Is 1 GB equal to 1 GiB?

No. 1 GB = 1,000,000,000 bytes (SI), while 1 GiB = 1,073,741,824 bytes (IEC).

Historical context

The IEC introduced binary prefixes (e.g., kibi-, mebi-) in 1998 to resolve confusion caused by misuse of SI prefixes for binary values. Despite this, many software tools still incorrectly label GiB as GB.

Practical applications

1. Cloud storage: A 1 TB plan (SI) offers 1,000 GB, but your OS shows ~931 GiB.
2. Internet speed: A 1 Gbps connection transfers $10^9$ bits/sec (SI), not $2^{30}$ bits.
3. Data Centers: A 10 Pbit network backbone (SI) handles 10,000,000,000,000,000 bits per second.

Common mistakes to avoid

• Assuming 1 GB = 1 GiB.
• Using SI formulas for memory-related calculations.
• Neglecting the 8x multiplier when converting bytes to bits.

By understanding these concepts, users can accurately compare storage capacities, bandwidth, and memory across platforms.