Number of States (n bits)
States = 2ⁿ
Quick answer
This calculator solves States = 2ⁿ for Number of States. With Number of Bits 1.1, the result is 2.144. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Each binary bit doubles the number of distinct values that can be represented, so n bits encode 2 to the n states. This sets the resolution of an ADC or DAC, the number of addressable memory locations from an address bus, the count range of a counter, and the size of any digital code space. It is the most fundamental relationship in digital design.
Variables
- States — Number of distinct values (codes)
- n — Number of bits
Practical Notes
A 10-bit ADC has 1024 levels; a 16-bit address bus reaches 65536 locations. Add one bit to double the range; the maximum unsigned value is 2ⁿ − 1.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| states | Number of States | — | — |
| n | Number of Bits | — | — |
Step by step
- 1. What you know: Number of Bits 1.1
- 2. The relation: States = 2ⁿ
- 3. Substitute: n = 1.1
- 4. Result: Number of States = 2.144
Worked examples
Minimum range
Given: Number of Bits 0.055
Result: Number of States = 1.039
Low range
Given: Number of Bits 0.55
Result: Number of States = 1.464
Typical
Given: Number of Bits 1.1
Result: Number of States = 2.144
High range
Given: Number of Bits 1.76
Result: Number of States = 3.387
Maximum range
Given: Number of Bits 17.6
Result: Number of States = 198700
Solving for each variable
Solve for Number of States
Number of Bits 0.055 → 1.039
Solve for Number of Bits
Number of States 0.025 → -5.322
How Number of States changes with Number of Bits
| Number of Bits (input) | Number of States (result) |
|---|---|
| 0.242 | 1.183 |
| 0.605 | 1.521 |
| 1.21 | 2.313 |
| 1.815 | 3.519 |
| 2.42 | 5.352 |
| 3.63 | 12.38 |
| 4.84 | 28.64 |
| 9.68 | 820.3 |
| 16.94 | 125700 |
| 24.2 | 1.93 × 10⁷ |
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<p><a href="https://vbatpower.com/formulas/number-of-states/">Number of States (n bits)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Number of States (n bits)?
Use States = 2ⁿ. With Number of Bits 1.1, Number of States works out to 2.144.
How do you calculate number of n states?
Rearrange for Number of States: with Number of Bits 0.55, Number of States is 1.464.
What is the formula for Number of States (n bits)?
The formula is States = 2ⁿ. Each binary bit doubles the number of distinct values that can be represented, so n bits encode 2 to the n states.
How do you find Number of Bits when you know the other values?
Rearrange for Number of Bits: with Number of States 0.025, Number of Bits is -5.322.
Related Concepts
All Digital Logic formulas →Need more features?
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