How do you calculate Number of States (n bits)?

Use the formula States = 2ⁿ. Each binary bit doubles the number of distinct values that can be represented, so n bits encode 2 to the n states. Enter the values you know in the calculator above and it solves for the remaining variable.

What is the formula for Number of States (n bits)?

The Number of States (n bits) formula is States = 2ⁿ, where States—Number of distinct values (codes); n—Number of bits.

What does States mean in the Number of States (n bits) formula?

States is Number of distinct values (codes).

Number of States (n bits)

States = 2ⁿ

Calculator

Number of States

Number of Bits

Result

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Formula

States = 2ⁿ

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.

Related Concepts

All Digital Logic formulas →

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