HP 15C Manual do Utilizador Página 38
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38 Section 3: The Memory Stack, LAST X, and Data Storage
Nested Calculations
The automatic stack lift and stack drop make it possible to do nested
calculations without using parentheses or storing intermediate results. A
nested calculation is solved simply as a series of one- and two-number
operations.
Almost every nested calculation you are likely to encounter can be done
using just the four stack registers. It is usually wisest to begin the
calculation at the innermost number or pair of parentheses and work
outward (as you would for a manual calculation). Otherwise, you may need
to place an intermediate result into a storage register. For example, consider
the calculation of
3 [4 + 5 (6 + 7)] :
Keystrokes
Display
6 v 7 +
13.0000
Intermediate result of
(6 + 7).
5 *
65.0000
Intermediate result of
5 (6 + 7).
4 +
69.0000
Intermediate result of
[4 + 5 (6 + 7)].
3 *
207.0000
Final result:
3 [4 + 5 (6 + 7)].
The following sequence illustrates the stack manipulation in this example.
The stack automatically drops after each two-number calculation, and then
lifts when a new number is keyed in. (For simplicity, throughout the rest of
this handbook we will not show arrows between the stacks.)
T
t
z
y
y
y
Z
z
y
x
x
y
Y
y
x
6
6
x
X
x
6
6
7
13
Keys:
6
v
7
+
- Owner’s Handbook 1
- Legal Notice 2
- Introduction 3
- Contents 4
- Contents 7 7
- 8 Contents 8
- Contents 9 9
- The HP-15C: 12
- A Problem Solver 12
- Manual Solutions 13
- Programmed Solutions 14
- Getting Started 18
- Prefix Keys 19
- Keying in Exponents 19
- The “CLEAR” Keys 20
- Display Clearing: ` and − 21
- Calculations 22
- 5998.0)]7.05.12()8.04.5[( 23
- Numeric Functions 24
- Trigonometric Operations 26
- Time and Angle Conversions 26
- Degrees/Radians Conversions 27
- Logarithmic Functions 28
- Hyperbolic Functions 28
- The Automatic Memory Stack 32
- LAST X, and Data Storage 32
- The LAST X Register and K 35
- Order of Entry and the v Key 37
- Nested Calculations 38
- Storage Register Operations 42
- Error 3 43
- Probability Calculations 47
- Random Number Generator 48
- Accumulating Statistics 49
- Standard Deviation 53
- Linear Regression 54
- Other Applications 57
- The Display 58
- Scientific Notation Display 59
- Engineering Notation Display 59
- Special Displays 60
- Digit Separators 61
- Error Display 61
- Overflow and Underflow 61
- Continuous Memory 62
- Resetting Continuous Memory 63
- Programming Basics 66
- Intermediate Program Stops 68
- Running a Program 68
- How to Enter Data 69
- Memory Configuration 75
- Initial Memory Configuration 76
- Program Boundaries 77
- Unexpected Program Stops 78
- Abbreviated Key Sequences 78
- User Mode 79
- Nonprogrammable Functions 80
- Program Editing 82
- Line Position 86
- to run 88
- Program Branching 90
- Example: Flags 95
- Looping 98
- Conditional Branching 98
- Subroutines 101
- Examples 102
- Further Information 105
- The Index Register 106
- The Mechanics 107
- Index Register Arithmetic 108
- Exchanging the X-Register 108
- Indirect Branching With V 108
- Indirect Flag Control With V 109
- Example: Loop Control with e 112
- test (goal) value 113
- Indirect Display Control 116
- Calculating With 120
- Complex Numbers 120
- Deactivating Complex Mode 121
- Entering Complex Numbers 121
- Stack Lift in Complex Mode 124
- Changing Signs 124
- Clearing a Complex Number 125
- Entering a Real Number 128
- One-Number Functions 131
- Two-Number Functions 131
- Stack Manipulation Functions 131
- Conditional Tests 132
- Error 0 133
- Problems 135
- )6 (-82 136
- For Further Information 137
- Calculating With Matrices 138
- Matrix Dimensions 140
- Dimensioning a Matrix 141
- Displaying Matrix Dimensions 142
- Changing Matrix Dimensions 142
- and R 146
- Matrix Operations 147
- The Result Matrix 148
- Copying a Matrix 149
- One-Matrix Operations 149
- Scalar Operations 151
- Arithmetic Operations 153
- Matrix Multiplication 154
- and BA 155
- Solving the Equation AX = B 156
- Calculating the Residual 159
- Using Matrices in LU Form 160
- 22222121 162
- 12121111 162
- 2 to transform Z 165
- Memory Allocation 171
- 4 to calculate X 172
- , -, * 173
- Summary of Matrix Functions 177
- Finding the Roots 180
- t / 20 185
- When No Root Is Found 186
- Error 8 187
- Choosing Initial Estimates 188
- letter label or G label 191
- Using _ in a Program 192
- Restriction on the Use of _ 193
- Memory Requirements 193
- Numerical Integration 194
- . )sin - ( cos 197
- dθθxxJ 197
- Accuracy of f 200
- 1.6054 ± 0.0001, the 201
- Using f in a Program 203
- Error Conditions 205
- Pr Error (Power Error) 208
- Stack Lift and 209
- Disabling Operations 210
- Enabling Operations 210
- Neutral Operations 211
- LAST X Register 212
- through R 214
- Memory Reallocation 215
- Restrictions on Reallocation 216
- Program Memory 217
- 23 if executed 218
- A Detailed Look at _ 220
- Error 8 is 221
- Accuracy of the Root 222
- produces a root of 223
- Interpreting Results 226
- routine has 229
- or any 229
- Finding Several Roots 233
- Limiting the Estimation Time 238
- For Advanced Information 239
- A Detailed Look at f 240
- )sin4cos( d 242
- )( xxfxF 246
- 10100.5)δ( 247
- (x) in roughly the same 248
- (x) ~ 10 248
- Batteries 259
- Function Summary and Index 262
- Computes natural 263
- Mathematics 264
- Matrix Functions 264
- Number Alteration 265
- Percentage 266
- Probability 266
- Manipulation 266
- Statistics 267
- Storage 267
- Trigonometry 268
- Programming Summary and Index 269
- Is flag set? Tests 270
- Subject Index 271
- Product Regulatory & 284
- Environment Information 284
- Logo, United States Only 285
- Canadian Notice 285
- Avis Canadien 285
- Chemical Substances 288
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