GB to bits converter

What is a Gigabyte (GB)?

A gigabyte (GB) is a decimal (base-10) unit of digital storage defined by the International System of Units (SI):

Usage:

• Storage devices (HDDs, SSDs) and internet service providers use GB to denote capacity or data transfer rates.

What is a Gibibyte (GiB)?

A gibibyte (GiB) is a binary (base-2) unit standardized by the International Electrotechnical Commission (IEC):

Usage:

• Operating systems like Windows use GiB but often mislabel it as “GB,” causing confusion.
• Correction: macOS typically displays storage in true SI units (GB), not GiB.

Key differences: SI (Base-10) vs. IEC (Base-2)

SI System (Decimal)

• Units: GB (gigabyte), TB (terabyte).
• Formula: $$1 \text{ GB} = 10^3 \text{ MB} = 10^6 \text{ KB} = 10^9 \text{ bytes}.$$

IEC system (binary)

• Units: GiB (gibibyte), TiB (tebibyte).
• Formula: $$1 \text{ GiB} = 2^{10} \text{ MiB} = 2^{20} \text{ KiB} = 2^{30} \text{ bytes}.$$

Difference:

Conversion formulas

GB to Bits (SI)

1. Convert GB to bytes: $$1 \text{ GB} = 10^9 \text{ bytes}.$$
2. Convert bytes to bits (1 byte = 8 bits): $$1 \text{ GB} = 10^9 \times 8 = 8,000,000,000 \text{ bits}.$$

General Formula:

GiB to Bits (IEC)

1. Convert GiB to bytes: $$1 \text{ GiB} = 2^{30} \text{ bytes}.$$
2. Convert bytes to bits: $$1 \text{ GiB} = 2^{30} \times 8 = 8,589,934,592 \text{ bits}.$$

General Formula:

Practical examples

Example 1: Converting 5 GB to Bits (SI)

Example 2: Converting 5 GiB to Bits (IEC)

Example 3: Internet Data Plan

A 100 GB monthly plan equals:

Why storage shows less capacity than advertised

A “1 TB” drive (SI units):

In IEC units:

Result: Windows displays ~931 GiB for a “1 TB” drive.

Common mistakes & clarifications

1. GB vs. GiB:
   • Storage marketed in GB (SI) but often displayed in GiB (IEC) by OS.
2. Bits vs. Bytes:
   • Network speeds (e.g., 100 Mbps) use bits; storage uses bytes.
3. OS-Specific Behavior:
   • Windows: Uses GiB but labels as “GB.”
   • macOS: Uses true GB (SI) for storage.

Historical context

• Pre-1998: SI prefixes (kilo, mega) were ambiguously applied to binary units.
• 1998: IEC introduced binary prefixes (kibi, mebi, gibi) to resolve confusion.

Frequently asked questions

How many bits are in 1 GB?

In the SI system:

Why does my 1 TB drive show only 931 GiB?

The drive uses SI units (1 TB = 10^{12} bytes), but Windows converts to IEC:

How to convert 3.5 GiB to bits?

Using the IEC formula:

What’s the practical difference between GB and GiB?

• 1 GB = 1,000,000,000 bytes (SI).
• 1 GiB = 1,073,741,824 bytes (IEC).
  Difference: ~7.37%.

Why are internet speeds measured in bits?

Bits per second (bps) standardize data transmission rates. Example:

Notes

• Storage devices: Marketed in SI units (GB/TB).
• Memory (RAM): Often uses IEC (GiB) but mislabeled as “GB.”
• Data transmission: Always measured in bits (e.g., Mbps).