Bit, Byte & Unit Conversions
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)