This is the English chapter of the original user manual of the TI-45 dated from 1977.
Scanned, transformed to ASCII via OCR and copied to HTML by F. Seebass, December 2001.
 


Texas Instruments

TI-45

Electronic Calculator

User Manual


TABLE OF CONTENTS

Description

Features and functions
Automatic clearing
Battery Considerations
Optional accessories

Keyboard Description

Calculator operation

Turning the calculator on
Initial display
Automatic turn off (Battery Saver)
Data entry
Input error correction
Scientific notation
Exponential shift
Error indication

Arithmetic functions

Combining operations (Calculator Hierarchy)
Parentheses
Calculations with a constant
Accuracy and rounding

Special functions

Roots and powers
Reciprocal
Natural logarithm and ex
Common logarithm and 10x
Trigonometric functions
Degree, Radian, Grad Conversions
Hyperbolic functions and Inverse

Memory usage

Notes on calculator operation

Service Information

Warrenty conditions

Examples


Description

The TI-45 slide-rule calculator produces an accurate electronic means of  obtaining answers to a wide range of problems beginning with elemental arithmetic and continuing through the most complicated of situations. Use this calculator regularly and it will soon become an inseparable component of your problem solving system.

Features and Functions

 
Arithmetic +, -, x,/ 4
Data entry +/-, pi 2
Display Scientific Notation
Exponent Increment
Exponent Decrement
3
Algebraic x2sqrt(x), 1/x, yx,xRoot(y) 5
Clearing Clear and Clear Entry 2
Data grouping  lOpen and close parentheses 3  (up to 15) and full algebraic hierarchy (up to 4 pending operations) 3
Memory Store, Recall, Sum, Exchange 4
Percent %, +%, -%, x%, :% 5
Trigonometric Sin, Cos, Tan, Sin-1, Cos-1, Tan-1, and 3 angular modes (Degrees, Radians, Grads) 9
Logarithmic ln x, log, ex, 10x 4
Constant Operates with +, -, x, ¸, yx and xRoot(y) 6



47

Battery considerations

The electronic battery (BP-9) provides about 4 hours of operation without recharging. About 6 hours of recharging will restore full charge when the calculator is off, 12 hours if the calculator is in use. When the battery becomes discharged, the display becomes dim or may flash or show erroneous symbols and numbers just before fading away.

Optional accessory

Electronic battery (BP-9) - Spare electronic batteries can be purchased separately.

Keyboard Description

On/clear Key - This key applies power to the calculator and allows input error correction (see chapter Input Error Correction).
[OFF] Off Key - Removes power from the calculator.
[0] through [9] Digit Keys - Enter numbers 0 through 9. See chapter Data entry.
[.] Decimal Point Key - Enters a decimaL point. See chapter Data entry.
[+/-] Change sign Key - Changes the sign of the mantissa and/or of the exponent.
[pi] Pi Key - Enters the value of pi correct to 11 digits. (This value is rounded to 8 digits for display only).
[+] Add Key* - Instructs the calculator to add the next entered quantity to the displayed number. See chapter Arithmetic Functions.
[-] Subtract Key* - Instructs the calculator to subtract the next entered quantity from the displayed number. See chapter Arithmetic Functions
[x] Multiply Key* - Instructs the calculator to multiply the displayed numbers by the next entered quantity. See chapter Arithmetic Functions.
[/] Divide Key* - Instructs the calculator to divide the displayed number by the next entered quantity. See chapter Arithmetic Functions.
[=] Equals Key - Completes all previously entered numbers and operations. This key is used to obtain both intermediate and final results. See chapter Arithmetic Functions.
[K] Constant Key - Stores a number and its associated operation for repetitive calculations. See chapter Calculations with a constant.
[(] [)] Parentheses Keys - Used to isolate particular numerical expressions for correct mathematical interpretation. See chapter Parentheses.
[yx] y to x Power Key - Raises the displayed value y to the xth power. See chapter Roots and Powers.
[x2] Square Key - Calculates the square of the number in the display. See chapter Roots and Powers
[sqrt(x)] Square Root Key - Calculates the square root of the number in the display. See chapter Roots and Powers.
[1/x] Reciprocal Key - Divides the display value into 1. See chapter Reciprocal.
[%] Percent Key - Converts displayed number from a percentage to a decimal. See chapter Percent.
[lnx] Natural logarithm - Calculates the natural logarithm (base e) of the number in the display. See chapter Natural logarithm.
[log] Common Logarithm - Calculates the common logarithm (base 10) of the number in the display. See chapter Common logarithm.
[DRG] Degree, Radian, Grad Key - Selects the units for angular measurement. Can be changed whenever desired. See chapter Degree, Radian, Grad Conversions.
[sin] Sine Key - Instructs the calculator to find the Sine of the displayed angle. See chapter Trigonometric functions.
[cos] Cosine Key - Instructs the calculator to find the cosine of the displayed angle. See chapter Trigonometric functions.
[tan] Tangent Key - Instructs the calculator to find the tangent of the displayed angle. See chapter Trigonometric functions.
[EE] Exponent Entry and Exponent/Decimal Shift Key - Allows entering and shifting down of the exponent. (Decrement). See chapters Scientific Notation and Exponential Shift.
[STO] Store Key - Stores the displayed quantity in the memory. See chapter Memory Usage.
[RCL] Recall Key - Retrieves stored data from the memory to the display. See chapter Memory Usage.
[SUM] Sum to Memory Key - Algebraically adds the displayed value to the memory content.. See chapter Memory Usage.
[EXC] Exchange Key - Exchanges the content of the memory with the displayed value. See chapter Memory Usage.
[INV] Iniverse Key - When pressed before yx, ln x, log, sin, cos, tan and EE, gives inverse functions respectively xRoot(y), ex, 10x, Arcsine, Arccosine, Arctangent. Exponent Increment (shifting). See chapters Exponential Shift, Roots and Powers, Trigonometric functions, Natural logarithm, Common logarithm.

* NOTE : Pressing one of these keys completes any previously entered divide or multiply, yx- or xRoot(y)-function.

Calculator operation

Your calculator is easy to operate because of its algebraic entry format which allows entry of most problems just as they are written. The following instructions and examples help you develop skill and confidence in problem solving.

Turning the Calculator On

Pressing  applies power to the calculator and totally clears the calculator. Power-on condition is indicated by the presence of a lighted digit in the display. The [OFF] key, of course, removes power from the calculator. When the battery is charged and the display is not blank, press [OFF] to clear the calculator

Initial Display

In addition to power-on and numerical information, the display provides indication of negative number, decimal point, overflow, underflow, angular mode and error. Numbers as large as 8 digits can be entered. All digit keys pressed after the 8th are ignored.

Any negative number displays a minus sign immediately to the left of the mantissa.

Automatic Turn-Off (Battery Saver)

Electronic control (as opposed to switch control) of ON and OFF, allows the calculator to minimize power consumption by displaying a number for only a limited length of time, then automatically turns the calculator completely off. This period of time is typically 7 to 10 minutes.

Data Entry

For maximum versatility, your calculator operates with a floating decimal point. When entering numbers, the decimal remains to the right of the mantissa until [.] is pressed and the integer part of the number is entered.

Numbers up to 8 digits in length can be entered into the calculator directly from the keyboard. The calculator can hold and work with 11 digits. Numbers of this length can be entered as the sum of two numbers.

Example : Enter 389182.70636
 
Enter Press Display
389182 [+] 389182
.70636 [=] 389182.17

Input Error Correction

At any point in a calculation,  can be pressed twice to clear all calculations including any errors and start over. This drastic action is seldom necessary.

If an incorrect number entry is made, pressing the key before any non-number key clears the incorrect number without affecting any calculation in progress.

Correction of an incorrect operation entry while there are incomplete operations in the calculator is dependent on the table below.
 
Inorrect Entry Desired Entry
+, - x yx xRoot(y)
+, - CT ON/C ON/C ON/C
x CT CT ON/C ON/C
yx CT CT - ON/C
xRoot(y) CT CT CT -

CK means to press the correct key and continue.

The  key in the table indicates that the incorrect entry cannot safely be corrected to the desired operation for all conditions so the problem must be restarted.

Scientific Notation

To enter very large or very small numbers you must use scientific notation where the number is entered as a mantissa multiplied by 10 raised to some power (exponent) such as -3.6089 x 10-32.

The entry procedure is to key in the mantissa (including its sign), then press [EE] and enter the power of ten.

The last two digits on the right side of the display are used to indicate the exponent of 10. Additional digits can be entered after pressing [EE] but only the last two numbers pressed are retained as the exponent

Regardless of how a mantissa is entered in scientific notation, the calculator normalizes the number, displaying a single digit to the left of the decimal point, when any function or operation key is pressed.

Example : Enter 6025 x 1020 .
 
Enter Press Display

0
6025 [EE] 6025. 00
20
6025. 20

[+] 6.025 23

The decimal point of the entered mantissa must not be beyond the 5th digit from the left because the mantissa for scientific notation is limited to 5 digits in the display. Eight digits can be entered, but only 5 are displayed when [EE] is pressed. The entire eight digit mantissa is used for calculations. It is possible to convert numbers of more than 5 digits on the condition to follow the instructions given under paragraph Notes on Calculator Operation.

Data in scientific notation form may be entered intermixed with data in standard form. The calculator converts the entered data for proper calculation.

Example: 3.2 x 103 + 12575.321 = 15775.321
 
Enter Press Display

0
3.2 [EE] 3.2 00
3 [+] 3.2 03
12575.321 [=] [x] 1.5775 04
1 [INV] [EE] [=] 15775.321

This example shows how the display can be removed from scientific notation format. If the displayed number is less than ± 9.9999 x 107 and larger than ± 1 x 107,  pressing [INV] [EE] then an operation after a number entry will produce a result in normal display format. Once a number is entered in scientific notation, the calculator will remain in scientific notation format until  is pressed or the above procedure performed.

Exponential Shift

The [EE] key can be used to alter the appearance of the displayed number without changing its value. When this key is pressed after a result is obtained or after a function or operation key is pressed, it decreases the exponent by one and moves the decimal point of the mantissa one place to the right. [INV] [EE] adds one to the exponent and moves the decimal one place to the left under the same conditions.

Example 1.2 x 1016 + 3.45 x 1014 = 1.2345 x 1016 =
              12.346 x 1015 = 1.2345 x 1016
 
Enter Press Display
1.2 [EE] 1.2 00
16 [+] 1.2 16
3.45 [EE] 3.45 00
14 [=] 1.2345 16

[EE] 12.345 15

[INV] [EE] 1.2345 16

Error indication

The display shows "Error" whenever the limits of the calculator are violated or when an improper mathematical operation is requested. When this occurs, any entry from the keyboard is not accepted until  is pressed. This clears the error condition and all pending operations. You must now return to the first of your problem and begin again.

Arithmetic functions

To perform simple addition, subtraction, multiplication or division, the calculator with in algebraic type of entry allows you to key in the problem just as it is stated.

It is a safe procedure to press the  key before the start of each new problem, unless [=] has been used to obtain the final result of a previous problem.

Combining Operations (Calculator hierarchy)

After a result is obtained in one calculation it may be directly used as the first number in a second calculation. There is no need to reenter the number from the keyboard.
In orderto efficiently combine operations, you need to understand the standard algebraic rules that have been specifically programmed into the calculator. These algebraic rules assign priorities to the various mathematical operations. Without a fixed set of rules, expressions such as 5 x 4 + 3 x 2 could have several meanings:
     5 x (4 + 3) x 2 = 70
or (5 x 4) + (3 x 2) = 26
or ((5 x 4) + 3) x 2 = 46
or 5 x (4 + (3 x 2) = 50

Algebraic rules state that multiplication is to be performed before addition. So, algebraically, the correct answer is (5 x 4) + (3 x 2) = 26. The complete list of priorities for interpreting expressions is:

  1. Special functions (trigonometric, logarithmic, square, square root, percent and reciprocal)
  2. Exponentiation (yx)- Roots (xRoot(y))
  3. Multiplication. Division.
  4. Addition. Subtraction.
  5. Equals
To illustrate, consider the interpretative order of the following example.

Example: 4 : 52x 7 + 3 x sin 30cos 60° = 3.2413203
 
Enter Press Display Comments
4 [/] 4. (4:) is stored.
5 [x2] 25 (52) - special function x2 evaluated immediately.

[x] 0.16 (4:52) evaluated because x is same priority as ¸.
7 [+] 1.12 x higher priority than +, so (4 : 52 x 7) evaluated. und + stored.
3 [x] 3. (3x) stored.
30 [sin] [yx] 0.5 Sin 30° evaluated immediately yx stored.
60 [cos] 0.5 Cos 60° evaluated immediately.

[=] 3.2413203 Completes all operations: sin 30cos 60° evaluated, then 3 x sin 30cos 60°next, then this is added to 1.12.

Thus, by entering the expression just as it is written, the calculator correctly interprets it as (4 : 52) x 7 + (3 x sin 30cos 60°). This enables to perform sum of products directly on the keyboard. When you have a special case where this hierarchy of interpretation does not give you the results you require, parentheses are available to clarify the mathematical expression for the calculator.

Parentheses

Parentheses should be used whenever a mathematical sequence cannot be directly entered using the previously mentioned algebraic rules or when there is doubt in your mind as to how the calculator is going to reduce an expression.

To illustrate the benefit of parentheses, try the following experiment: press [(] [x] [)] and you will see the value 35 displayed. The calculator has evaluted 5 x 7 and replaced it with 35 even though the [=] key was not pressed Because of this function of parentheses, the algebraic rules now apply their hierarchy of operations to each set of parentheses. Use of parentheses insure that your problem can be keyed in just as you have written it down. The calculator remembers each operation and evaluates each part of the expression as soon as all necessary information is available. When a closed parenthesis is encountered, all operations back to the corresponding open parenthesis are completed.

Example : 4 x (5 + 9) (7 - 4)(2+3) = .23045268

Key in this expression and follow the path to completion.
 
Enter Press Display Comments
4 [x] [(] 4. (4x) stored pending evaluation of parentheses
5 [+] 5. (5+) stored
9 [)] 14. (5 + 9) evaluated

[/] 56. Hierarchy evaluates 4 x 14.

[(] 56. (56:) stored pending evaluation of parentheses
7 [-] 7. (7-) stored
4 [)] 3. (7-4) evaluated

[yx] [(] 3. Prepares for exponent
2 [+] 2.
3 [)] 5. (2 + 3) evaluated

[=] .23045268 (7-4)(2+3) evaluated 4 x (5 + 9)

As many as fifteen parentheses can be open at any one time and four operations can be pending. If you do attempt to open more than 15 parentheses or if the calculator tries to store more than four operations, the error message appears in the display.

Each time a closed parenthesis is encountered, the contents are evaluated back to the nearest open parenthesis and are replaced with a single value. Specifically, you can check intermediate results. Note that in all the examples, the expressions are entered in a straight left to right sequence.

Calculations with a Constant

To use the constant feature, enter the repetitive number, m, then enter the desired operation, then press [K].
 
m [+] [K] adds m to each subsequent entry.
m [-] [K] subtracts m from each subsequent entry.
m [x] [K] multiplies each subsequent entry by m.
m [/] [K] divides each subsequent entry by m.
m [yx] [K] raises each subsequent entry to the m power.
m [INV] [yx] [K] takes the mth root of each subsequent entry.

After storing the constant, each calculation is completed by entering the new number and pressing [=]. Clearing the calculator or entering any of the above arithmetic functions eliminates the constant that is currently stored.

Accuracy and Rounding

Each calculation produces an 11-digit result. The result is rounded to an 8-digit standard display or to 5 digits for scientific notation. The 5/4 rounding technique built into this calculator adds 1 to the least significant digit of the display if the next, non displayed digit is five or more. If this digit is less than five, no rounding is applied.

The higher mathematical functions use iterative calculations. The cumulative error from these calculations in most cases is maintained beyond the eight-digit display so that no inaccuracy is displayed.

Most calculations are accurate to ±2 in the eighth digit as long as the calculator is not in scientific notation. The only exceptions are the tangent function as it approaches undefined limits and yx where y is within 10-6 of 1.

Special functions

Single-variable functions operate on the displayed value instantly, replacing the displayed value with its function. These functions do not interfere with my calculations in progress and can therefore be used at any point in a calculation.

Roots and Powers

The square key [x2] calculates the square of the number x in the display.
The square root key [sqrt(x)] calculates the square root of the number x in the display.

Universal powers are accessed by the [yx] key and roots are accessed by [INV] [yx] key sequence providing xRoot(y).
These functions are the only special functions that do not act on the displayed value immediately. They require a second value before the function can be realized. Enter y, press [yx] or [INV] [yx], enter x and press [=] or an arithmetic function key to yield the answer.

There is a restriction on these functions - the variable y must be non-negative. When y is negative "Error" lights up on the display after x and an operation key is pressed. Any non-negative number taken to the zero power is 1.

Reciprocal

The reciprocal key [1/x] divides the display value x into 1. x 0.

Percent

The percent key [%] converts the displayed number from a percentage to a decimal .

When [%] is pressed after an arithmetic operation, add on, discount and percentage can be computed as follows:

[+][%] [=]: adds n % to the number displayed
[-][%] [=]: subtracts n % from the number displayed
[x][%] [=]: multiplies by n % the number displayed
[/][%] [=]: devides by n % the number displayed
 

Natural logarithm and ex

The key [lnx] calculates the natural logarithm (base e) of the number x
in the display.  x > 0.
The sequence [INV] [lnx] calculates the natural antilogarithm (e to the x power) of the number in the display.

Common logarithm and 10x

The key  [log] calculates the common logarithm (base 10) of the number x in the display. x>0.
The sequence [INV] [log] calculates the natural antilogarithm (10 to the x power) of the displayed value.

Trigonometric functions

The degree, radian, grad key [DRG] selects the units for angular measurement. When turned on, the calculator is in the degree mode. Pressing the [DRG] key, once places it in the radian mode, twice in the grad mode. Another key push returns the calculator to the degree mode. Another key push returns the calculator to the degree mode.
The display indicates the current angular mode of the calculator. An apostrophe (') in the far left side of the display denotes the radian mode while quote marks (") indicate the grad mode. If the apostrophe and quotes are absent, angles are measured in degrees.
The angular mode has absolutely no effect on calculations unless the trigonometric functions are being used.
When the trig functions (sine, cosine, and tangent) are activated, they find their respective functions of the angle in the display. The inverse trig functions find the smallest angle whose function is in the display. Trigonometric values can be calculated for angles greater then one revolution. As long as the trigonometric function is displayed in normal form rather than in scientific notation all display digits are accurate for any degrees. -200 p to +200 p radians and -40000 to 40000 grads.
The tangent of ± 90°,  ±p/2 radians or ± 100 grads results in an error condition. As the tangent approaches these undefined limits the accuracy is restricted.
The largest angle resulting from an arc function is 180 degrees (p radians or 200 grads). Because certain angles have identical function values within one revolution, the angle returned by each function is restricted as follows:
 
Arc Function Quadrant
arcsin x, arccos x, arctan x First
arcsin -x, arctan -x Fourth
arccos -x Second

Degree, Radian, Grad Conversions

Conversion Key Sequence
Degrees to Radians
Radians to Grads
Grads to Degrees
[sin] [DRG] [INV] [sin]
Degrees to Grads
Grads to Radians
Radians to Degrees
[sin] [DRG] [DRG] [INV] [sin]

The angular range of the above conversions must be limited to the first
and fourth quadrants. Larger angles are returned in those quadrants.

Hyperbolic Functions

Solving problems involving hyperbolic functions uses the exponential ([INV] [lnx]) capability of your calculator.
 
Hyperbolic Sine (sinh) x =  1/2 (ex-e-x = e2x - 1

2ex
Hyperbolic Cosine (cosh) x = 1/2 (ex+e-x = e2x + 1

2ex
Hyperbolic Tangent (tanh) x = ex - e-x 

ex + e-x
= e2x - 1

e2x + 1

Inverse Hyperbolic Functions

sinh-1x  = ln(x +Ö(x2 + 1))

cosh-1x  = ln(x +Ö(x2 - 1))
 
tanh-1x = 1/2 ln 1 + x

1 - x

Memory usage

The memory keys allow data to be stored and retrieved at will for additional flexibility in calculations. Use of the memory does not affect any calculations in progress, so memory operations can be used wherever needed.

The Store key [STO] stores the displayed quantity in the memory without removing it from the display. Any previously stored value is cleared.

The Recall key [RCL] retrieves stored data from the memory to the display. Use of this key does not clear the memory.

The Sum to Memory key [SUM] algebraically adds the displayed value to the memory contents.
Important: The clear key  does not clear the memory except when the calculator is first turned on. Therefore the first quantity should be stored using [STO], or a zero should be stored to ensure the memory is empty before using [SUM].
This key is used to accumulate the results from a series of independant calculations. [SUM] replaces the arithmetic sequence [+] [RCL] [=] [STO].

The exchange key [EXC] swaps the content f the memory with the displayed value. The displayed value is stored and the previously stored value is displayed.
This key combines the store and recall operations into a single key. Use of this key, like the other memory keys, does not disturb a sequence of calculations and can consequently be used anywhere in the solution of  a problem.

Notes on calculator operation

1. When using the exponential shift feature of your calculator and the display does not shift to the position requested, simply press [=] to restore the normalized display and begin shifting again (to retain pending operations, press [EXC] twice instead). Attempting to shift into a mantissa with more than five digits in the integer portion of the display is not possible. See chapter Exponential shift for additional information.

2. Attempting to use a number greater than 1 x 1099 as the first operand in multiplication may result in "Error" condition although the product is within the capacity of the calculator.

Example: 2 [EE] 99 [x] .6 [=] "Error".
The problem may be solved in the reversed order,
Example: .6 [x][EE] 99 [=] 1.2 99 (=1.2 x 1099).

3. Any entry in scientific notation with a negative zero exponent can cause erroneous results.
Example : 2 [EE] [+/-] [yx][=] 4 - 04

Service information

In Case of difficulty

1. Check to be sure the battery pack is properly attached to the calculator and that the adapter/charger is connected to a live electrical outlet.
CAUTION: Use of other than a 9 volt BP9 electronic battery may apply improper voltage to your TI-45 calculator and will cause damage.
Use only the AC 9900R Adapter/Charger (9900R U.K. for U.K.).

 2. If the display contains only a decimal point moving across the window, the calculator has automatically lapsed into a power saving mode. The value that was present in the display can be easily retrieved and displayed by pressing the exchange key [EXC] twice. This procedure does not adversely affect any calculation in progress.

3. If the display fails to light, check for an improperly inserted or dischanged battery pack. Also try to unplug and reinsert the battery connector. See chapter Battery considerations.

4. When a battery pack is inserted into the calculator and the display is not blank, pressing [OFF] should blank the display and prepare the calculator for your use.

5. Review operating instructions to be certain calculations are performed correctly.

One-year-limited warrenty

The TI-45 electronic calculator (including charger) from Texas Instruments is warranted to the original purchaser for a period of one (1) year from the original purchase data under normal use and service - against defective materials or workmanship.

This warranty is void if: the calculator has been damaged by accident or unreasonable use, neglect, improper service or other causes not arising out of defects in material or workmanship.

TEXAS INSTRUMENTS SHALL NOT BE LIABLE FOR LOSS OF USE OF THE CALCULATOR OR OTHER INCIDENTAL OR CONSEQUENTIAL COSTS, EXPENSES OR DAMAGES INCURRED BY THE PURCHASER.

During the above one-year period, the calculator or its defective parts will be repaired, adjusted and/or replaced with a reconditioned model of equivalent quality ("REFURBISHED") at manufacturer's option without charge to the purchaser when the calculator is returned, prepaid and insured, with proof-of-purchase date, to Texas Instruments. UNITS RETURNED WITHOUT PROOF-OF-PURCHASE DATE WILL BE REPAIRED AT THE SERVICE RATES IN EFFECT AT THE TIME OF RETURN.

In the event of replacement with a reconditioned model, the replacement unit will continue the warranty of the original calculator product or 90 days whichever is longer.

THIS WARRANTY OFFERS YOU SPECIFIC LEGAL RIGHTS AND DOES NOT AFFECT ANY STATUTORY CONSUMER RIGHTS.

IMPORTANT: Before returning your calculator for repair, carefully review service and mailing instructions in this manual.