# Knowledge Base

## Solution 12705: Differences Between Algebraic Operating System (AOS) and Equation Operating System (EOS).

### What are the differences between Algebraic Operating System (AOS) and Equation Operating System (EOS)?

The Equation Operating System (EOS) defines the order in which functions and expressions are entered and evaluated on many of our calculators. This feature lets the user enter functions and expressions in a simple, straightforward sequence.

EOS evaluates functions and expressions in this order:

1) Functions that precede the argument, such as square root(, sin(, or log(.
2) Functions that are entered after the argument, such as exponents, factorials, r (radians), ° (degrees), and unit conversions.
3) Powers and roots, such as 2^5.
4) Permutations (nPr) and combinations (nCr).
5) Multiplication, implied multiplication and division.
7) Relational functions, such as > or <.
8) Logic operator "and".
9) Other logic operators, such as "or", "not" and "xor".

Within a priority level, EOS evaluates from left to right. Calculations within parenthesis are always evaluated first.

The following calculators use EOS:

• TI-Nspire™ family handhelds.

• TI-73 Explorer™, TI-80, TI-81, TI-82, TI-83 family, TI-84 Plus family (TI-Nspire handheld in TI-84 Plus mode).

• TI-85, TI-86.

• TI-89 family, TI-92 family, Voyage 200.

• TI-34 II Explorer Plus™, TI-34 MultiView™, TI-30X IIS/B, TI-30XS/TI-30XB MultiView™, TI-36X II, TI-36X Pro.

• TI-10, TI-15 Explorer™

The Algebraic Operating System (AOS) completes all operations according to their relative priorities, which are listed below:

1) Trigonometric and hyperbolic functions, square roots, cube roots, factorials, reciprocals (inverse), angle conversions, combinations, permutations, percents, logarithms, sign changes (+/-), metric conversions, logical "not".
2) Universal powers, exponents and roots.
3) Multiplication and division.
5) Logical "and".
6) Other logical functions, such as "or", "xor" and "xnor".
7) Close parenthesis.
8) Equals.

Operations of priority 1 are immediate functions which means they are performed as soon as the operation keys are pressed.

Operations in priorities 2, 3, and 4 are completed by any operation with the same priority or with a lower priority.

The [=] key completes all operations.

The following calculators use AOS:

• Explorer Plus™, Math Explorer™, MathMate™

• TI-30X (and Solar), TI-30Xa (and Solar), TI-30Xa SE™, TI-34, TI-35X, TI-36X Solar.