Bit, Byte & Unit Conversions
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The decimal prefixes used here (kilo, mega, giga…) are the standard SI prefixes applied to bytes. The binary prefixes (kibi, mebi, gibi…) are the IEC equivalents specifically for powers of 2.
Bit & Byte Basics
| Unit | Symbol | In Bits | In Bytes |
|---|---|---|---|
| Bit | b | 1 | 0.125 |
| Byte | B | 8 | 1 |
Further Info: Network speeds use bits/s (Mb/s, Gb/s), storage uses bytes (MB, GB)
Decimal Units (Base 10)
| Unit | Symbol | Power | Factor | In Bytes |
|---|---|---|---|---|
| Kilobyte | kB | 10³ | 1,000¹ | 1,000 |
| Megabyte | MB | 10⁶ | 1,000² | 1,000,000 |
| Gigabyte | GB | 10⁹ | 1,000³ | 1,000,000,000 |
| Terabyte | TB | 10¹² | 1,000⁴ | 1,000,000,000,000 |
| Petabyte | PB | 10¹⁵ | 1,000⁵ | 1,000,000,000,000,000 |
Step: One step is worth '³'
Used by: Hard drive manufacturers, marketing, networking
Binary Units (Base 2)
| Unit | Symbol | Power | Factor | In Bytes |
|---|---|---|---|---|
| Kibibyte | KiB | 2¹⁰ | 1,024¹ | 1,024 |
| Mebibyte | MiB | 2²⁰ | 1,024² | 1,048,576 |
| Gibibyte | GiB | 2³⁰ | 1,024³ | 1,073,741,824 |
| Tebibyte | TiB | 2⁴⁰ | 1,024⁴ | 1,099,511,627,776 |
| Pebibyte | PiB | 2⁵⁰ | 1,024⁵ | 1,125,899,906,842,624 |
Step: One step is worth '¹⁰'
Used by: Operating systems, RAM, actual storage calculations
Conversion Methods
1. Bit ↔ Byte
Bit → Byte
Formula: bits ÷ 8 = bytes
Example: 64 bits → bytes
64 ÷ 8 = 8 bytes
Byte → Bit
Formula: bytes × 8 = bits
Example: 100 bytes → bits
100 × 8 = 800 bits
2. Decimal Units (Using 1,000)
Upward (Smaller → Larger)
Steps: kB → MB → GB → TB → PB
Formula: value ÷ 10^steps
Example: 5,000,000 kB → GB
Steps: kB → MB → GB = 2 steps
5,000,000 kB ÷ 10⁶ = 5 GB
Downward (Larger → Smaller)
Steps: PB → TB → GB → MB → kB
Formula: value × 10^steps
Example: 2 TB → MB
Steps: TB → GB → MB = 2 steps
2 TB × 10⁶ = 2,000,000 MB
3. Binary Units (Using 1,024)
Upward (Smaller → Larger)
Steps: KiB → MiB → GiB → TiB → PiB
Formula: value ÷ 2^steps
Example: 6,800,000 KiB → GiB
Steps: KiB → MiB → GiB = 2 steps
6,800,000 KiB ÷ 2²⁰ = 6.485 GiB
Downward (Larger → Smaller)
Steps: PiB → TiB → GiB → MiB → KiB
Formula: value × 2^steps
Example: 3 GiB → KiB
Steps: GiB → MiB → KiB = 2 steps
3 GiB × 2²⁰ = 3,145,728 KiB
4. Decimal ↔ Binary Conversion
Decimal → Binary (e.g., MB → MiB)
Formula: (decimal value) ÷ 1.024^steps ≈ binary value
Example: 1,000 MB → MiB
Steps: Both are "Mega" level = same position, but different base
1,000 MB ÷ 1.024 ≈ 976.56 MiB
Alternative (precise):
1,000 MB * 10⁶ = 1,000,000,000 bytes
1,000,000,000 bytes ÷ 2¹⁰ = 953.67 MiB
Binary → Decimal (e.g., GiB → GB)
Formula: (binary value) × 1.024^steps ≈ decimal value
Example: 500 GiB → GB
Steps: Both are "Giga" level = same position, but different base
500 × 1.024 ≈ 512 GB
Alternative (precise):
500 GiB * 2³⁰ = 536,870,912,000 bytes
536,870,912,000 bytes ÷ 10⁹ = 536,87
Quick Reference
| Conversion Type | Formula | Example |
|---|---|---|
| Bit → Byte | ÷ 8 | 1,000 b → 125 B |
| Byte → Bit | × 8 | 125 B → 1,000 b |
| Decimal Up | ÷ 10^steps | 5,000 MB → 5 GB |
| Decimal Down | × 10^steps | 2 TB → 2,000,000 MB |
| Binary Up | ÷ 2^steps | 2,048 KiB → 2 MiB |
| Binary Down | × 2^steps | 3 GiB → 3,145,728 KiB |
| MB → MiB | ÷ 1.024 | 1,000 MB ≈ 976.56 MiB |
| GiB → GB | × 1.024 | 500 GiB ≈ 512 GB |
Common Pitfalls
- Don't mix units:
1 GB ≠ 1 GiB(1 GB = 0.931 GiB) - Marketing trick: A "500 GB" hard drive is actually ~465.66 GiB
- Network speeds: 100 Mb/s ≠ 100 MB/s (100 Mb/s = 12.5 MB/s)
See Also
- SI Prefixes: the general metric prefixes (kilo, mega, giga, milli, micro, etc.) applied to any unit, not just bytes