# Unit 11 Level Change Indicators

Mathematical expressions containing superscript or subscript characters, such as exponents or bases, appear raised or lowered from the baseline in print.

# Examples:

X^{2}

B_{12}

In Nemeth Code, level change indicators show when a number, letter, or other expression is raised or lowered, and when it returns to the original baseline.

Superscript Indicator | ⠘ |

Subscript Indicator | ⠰ |

Baseline Indicator | ⠐ |

Multipurpose Indicator | ⠐ |

# Superscript

When a mathematical expression contains a raised character, the superscript indicator (dots 4-5) is placed directly in front of the character or expression to indicate a level change above baseline. The level change remains in effect until it is terminated by the next space, although the space may be preceded by a comma.

# Examples:

9^{3}

⠼⠔⠘⠒

x^{2}

⠭⠘⠆

4^{4} = 64

⠼⠲⠘⠲⠀⠨⠅⠀⠼⠖⠲

2^{2}, 3^{2}, 4^{2}

⠼⠆⠘⠆⠠⠀⠼⠒⠘⠆⠠⠀⠼⠲⠘⠆

The correct answer is 2 x 2 = 2^{2}.

⠠⠮⠀⠉⠕⠗⠗⠑⠉⠞⠀⠁⠝⠎⠺⠻⠀⠊⠎⠀⠸⠩⠀⠼⠆⠈⠡⠆⠀⠨⠅⠀⠼⠆⠘⠆⠠⠀⠸⠱⠲

* Notice that this example is written with Nemeth Code switch indicators.

# Non-Use of Superscript with Ordinal Numbers:

The superscript indicator is not used with raised ordinal numbers, such as ^{st} or ^{th}. They are not considered superscript and are transcribed on the baseline.** **

# Example:

1^{st}, 2^{nd}, 3^{rd}, 4^{th}

⠼⠂⠎⠞⠠⠀⠼⠆⠝⠙⠠⠀⠼⠒⠗⠙⠠⠀⠼⠲⠞⠓

# Subscript

Like the superscript indicator, the subscript indicator (dots 5-6) is placed directly in front of a character or expression to indicate a level change below baseline.

# Examples:

53_{6}

⠼⠢⠒⠰⠖

P_{(y+4)}

⠠⠏⠰⠷⠽⠬⠲⠾

x_{y}

⠭⠰⠽

# Subscript Indicator Exception

The subscript indicator is omitted when a baseline character is a letter or abbreviated function name and the subscript is a number.

# Examples:

CO_{2}

⠠⠉⠠⠕⠆

A_{3}

⠠⠁⠒

* Notice that the next two examples are written with Nemeth Code switch indicators.

H_{2}O = water.

⠸⠩⠀⠠⠓⠆⠠⠕⠀⠨⠅⠀⠸⠱⠀⠺⠁⠞⠻⠲

Solve for x; log_{10 }x

⠠⠎⠕⠇⠧⠑⠀⠿⠀⠰⠭⠆⠀⠸⠩⠀⠇⠕⠛⠂⠴⠀⠭⠀⠸⠱** **

(log is an abbreviated function name for logarithm)

# Baseline Indicator

If a character(s) above or below baseline is not followed by a space, a baseline indicator (dot 5) is required to indicate that the next character is no longer raised or lowered. The baseline indicator is placed directly after the character(s) affected by the level change.

# Examples:

B^{2}+2a

⠠⠃⠘⠆⠐⠬⠆⠁

* Notice that without returning to baseline after the exponent, the above expression would be read B^{2+2a}.

X^{2 }+ Y^{2} =

⠠⠭⠘⠆⠐⠬⠠⠽⠘⠆⠀⠨⠅

* Notice that the baseline indicator is used for the first term, X, but since there is a space after the second term, Y, a baseline indicator is not needed.

(5 x 4^{2})

⠷⠢⠈⠡⠲⠘⠆⠐⠾

* Notice that the baseline indicator is needed before the closing parentheses because the parenthesis applies to the baseline expression.

a^{2}b

⠁⠘⠆⠐⠃

* Without the baseline indicator this would have been read as: a^{2b}

⠹⠭⠘⠆⠐⠌⠽⠘⠆⠐⠼

* Without the baseline indicator this would have been read as:

${x}^{{\displaystyle \frac{2}{y\#}}}$# Degree Symbol

Degree (°) | ⠘⠨⠡ |

The degree symbol (°) is a raised hollow dot. It is formed by placing the superscript indicator in front of the hollow dot symbol. If the degree symbol is not followed by a space, a baseline indicator is used to return to baseline.

# Examples:

A circle = 360°.

⠠⠁⠀⠸⠩⠀⠉⠊⠗⠉⠇⠑⠀⠨⠅⠀⠼⠒⠖⠴⠘⠨⠡⠀⠸⠱⠲

Boiling water is 212° F (100° C).

⠠⠃⠕⠊⠇⠬⠀⠺⠁⠞⠻⠀⠊⠎⠀⠸⠩⠀⠼⠆⠂⠆⠘⠨⠡⠀⠰⠠⠋⠀⠷⠂⠴⠴⠘⠨⠡⠀⠰⠠⠉⠾⠀⠸⠱⠲

90°-60° = 30°

⠼⠔⠴⠘⠨⠡⠐⠤⠖⠴⠘⠨⠡⠀⠨⠅⠀⠼⠒⠴⠘⠨⠡

* Notice the use of the baseline indicator.

# Brain Boost

# Raised +/- signs

A mathematical expression with a raised positive or negative sign requires a superscript indicator to show the level change. A baseline indicator must be used to return the expression to baseline after the raised sign.

**Examples:**

^{+}5

⠘⠬⠐⠢

^{-}20° F

⠘⠤⠐⠆⠴⠘⠨⠡⠀⠰⠠⠋

Solve 24 + ^{-}17 =

⠠⠎⠕⠇⠧⠑⠀⠸⠩⠀⠼⠆⠲⠬⠘⠤⠐⠂⠶⠀⠨⠅⠀⠸⠱

10 - ^{-}6 =

⠼⠂⠴⠤⠘⠤⠐⠖⠀⠨⠅

* Notice that the use of the baseline indicator separates the minus sign and the negative sign.

# Multipurpose Indicator

Dot 5 serves several other functions in addition to the baseline indicator and is called the Multipurpose Indicator (MI). It is used when there is a need for added clarification. It is used when a number follows a letter that could be misinterpreted as subscript. The multipurpose indicator reinforces or clarifies the baseline status of the number.

# Examples:

a1

⠁⠐⠂

B52

⠠⠃⠐⠢⠆

* Without the MI, it could be read as B_{52}

A multipurpose indicator is also used in front of a punctuation indicator that follows a tally mark to clarify the meaning (both the tally mark and the PI are dots (4-5-6).

# Example:

||||| ||||| ||.

⠸⠸⠸⠸⠸⠀⠸⠸⠸⠸⠸⠀⠸⠸⠐⠸⠲

* Or it would look like another tally mark.