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Number Systems
Appendix B
B3
The binary numbering system uses a number set that consists of two
digits: the numbers 0 and 1. All information in memory is stored as an
arrangement of 1 and 0.
Each digit in a binary number has a certain place value expressed as a
power of two (Figure B.3). The decimal equivalent of a binary number is
computed by multiplying each binary digit by its corresponding place
value and adding these numbers together.
By grouping several binary digits together, values can be formed to
represent decimal or octal numbers.
Figure B.3
Binary
Numbering System
1 x 2
7
= 128
1 x 2
6
= 64
1 x 2
5
= 32
0 x 2
4
= 0
1 x 2
3
= 8
1 x 2
2
=
4
1 x 2
1
= 2
1 x 2
0
=
1
11101111
128
64
32
8
4
2
1
239
10
11101111
2
=
239
10
2
B.3
Binary Numbering System
- Important User Information 2
- Table of Contents 3
- to Programming 4
- Table of Contents iii 5
- Table of Contentsiv 6
- 111. . . . . . . 7
- Table of Contentsvi 8
- Table of Contents vii 9
- Table of Contentsviii 10
- Introduction 11
- Chapter 1 12
- Capabilities 13
- Additional Publications 15
- Terms Used in This Manual 16
- Hardware Considerations 17
- Diagnostic 18
- Indicators 18
- Select Switch 18
- RunTime 19
- Processor Diagnostic 20
- PowerUp 21
- Recovery 21
- Switch Group Assembly 21
- Last State Switch 22
- I/O Rack Number 22
- Industrial Terminal 23
- Local System Structure 23
- Remote System Structure 24
- Local/Remote 25
- Structure 25
- Chapter 2 26
- Data Table 28
- Memory Organization 29
- Data Table Areas 31
- Processor Work Areas 1 and 2 31
- Output Image Table 32
- Input Image Table 33
- Chapter 3 34
- Developing the Data Table 38
- Displaying the Data Table 38
- Data Table Area Configuration 39
- Configuring The Data Table 39
- Changing Data Table Areas 41
- Memory Write Protect 42
- User Program 43
- Instruction Address 45
- Fundamental Operation 48
- DESCRIPTION 52
- BIT NUMBER 52
- 17 1007 00 52
- STARTING WORD ADDRESS 52
- Data Table Bit Assignments 53
- Sequencer Table Bit 54
- Assignments 54
- I/O Assignments 55
- Timer/Counter Assignments 56
- Data Storage Assignments 56
- File Storage 57
- ALLEN-BRADLEY 58
- Connection Diagram Addressing 58
- Bulletin 1771 I/O Chassis 59
- (16-point Modules) 59
- Programmable Controller 60
- Introduction to Programming 65
- Ladder Diagram Logic 66
- RelayType Instructions 67
- Examine Instructions 67
- Examine Off Instruction 68
- Output Instructions 69
- Branch Instructions 73
- Solution 74
- Ending a Program 76
- Programming RelayType 77
- Operating Instructions 78
- Directories 79
- Searching 80
- Single Rung Display 82
- Incomplete Rung 82
- Remote Mode Select 83
- Inserting an Instruction 84
- Removing an Instruction 85
- Inserting a Rung 85
- Removing a Rung 85
- Without Data 86
- Online Data Change 86
- OnLine Programming 87
- Data Initialization Key 88
- Chapter 4 89
- Insert an Instruction 90
- Remove an Instruction 91
- Insert a Rung 91
- Remove a Rung 92
- Correct an Error 93
- Clearing 94
- Data Table Clear 95
- User Program Clear 95
- Partial Memory Clear 95
- Program Recommendations 96
- Figure 5.1 99
- Timer Instructions 100
- Timer OnDelay Instruction 101
- Timer OffDelay Instruction 103
- Retentive Timer Instruction 104
- Chapter 5 106
- UpCounter Instruction 107
- Counter Reset Instruction 109
- DownCounter Instruction 110
- Scan Counter Instruction 111
- Program for Determining 116
- FiletoFile 120
- Move and File 120
- Complement 120
- Logic Instructions 121
- FiletoFile AND, OR, XOR 121
- Data Transfer Instructions 124
- Get Instruction 124
- Put Instruction 125
- Data Comparison 126
- Instructions 126
- Les and Equ Instructions 126
- Get Byte and Limit Test 129
- Get Byte-Put Instruction 130
- Programming Data 131
- Manipulation Instructions 131
- Arithmetic Instructions 133
- Add Instruction 134
- Subtract Instruction 135
- Multiply Instruction 136
- Divide Instruction 136
- Programming Arithmetic 137
- BCD to Binary Conversion 138
- Programming a BCD to 139
- Binary Conversion 139
- Instruction 139
- BinarytoBCD Conversion 140
- Programming a Binaryto 140
- BCD Conversion Instruction 140
- I/O Updates 145
- Scan Sequence 145
- Immediate Input Instruction 147
- Immediate Output 148
- Programming 150
- Immediate I/O 150
- Remote Fault Zone 151
- Dependent Programming 154
- Independent Programming 155
- Watchdog Timer 158
- Peripheral Functions 160
- Contact Histogram 161
- On Time Off Time On Time 162
- Chapter 8 163
- Loading Memory from a 166
- Data Cartridge Tape 166
- Report Generation 169
- Chapter 9 170
- Commands 171
- Message Control Word File 172
- Store - MS 173
- Print - MP 174
- [Attribute #] [T] 178
- Manually Initiated Report 179
- Generation 179
- Automatic Report 180
- Messages 181
- Additional Messages 181
- Example Programming 182
- Block Transfer 184
- Address of Preset Value ↔ 100 186
- Above Data Address 186
- Block Transfer Instructions 187
- Data Address and Module 187
- Block Length 188
- File Address 188
- Chapter 10 189
- Multiple Reads of Different 191
- Block Lengths from One 191
- Defining the Block Transfer 194
- Data Address Area 194
- Buffering Data 195
- Bidirectional Block Transfer 197
- Operation 197
- Considerations 201
- Jump Instructions and 202
- Subroutine Programming 202
- Chapter 11 204
- Label Instruction 207
- Jump to Subroutine 208
- Subroutine 211
- Nested Subroutines 212
- Return Instruction 215
- Chapter 216
- File Planning 217
- File Instructions 217
- Externally Indexed Counter 219
- Internally Indexed Counter 219
- Complete Mode 220
- Distributed Complete Mode 222
- Incremental Mode 225
- File Instruction RunTime 227
- FiletoFile Move 227
- Programming FiletoFile 229
- Move Instructions 229
- FiletoWord 230
- Programming FiletoWord 231
- WordtoFile 233
- Data Monitor Mode 236
- Accessing the Data Monitor 236
- Figure 12.20 237
- Data Monitor Display 239
- Cursor Controls 240
- Data Monitoring Procedures 241
- Entering and Changing Data 242
- Shift Register Instructions 244
- Shift File Up 245
- Programming Shift File Up 246
- Shift File Down 248
- Programming Shift File 248
- Down Instruction 248
- FIFO Load and FIFO Unload 249
- Programming FIFO Load 251
- Bit Shifts 253
- Programming Bit Shift Left 255
- Bit Shift Right 257
- Chapter 14 258
- File – Starts at word 400 259
- Examine On Shift Bit 260
- Programming Examine On 260
- Shift Bit Instruction 260
- Set Shift Bit 261
- Programming Set Shift Bit 261
- Reset Shift Bit 262
- Programming Reset Shift Bit 263
- Sequencer Instructions 264
- Sequencer Output 266
- Sequencer Output Analogy 266
- Operation of the Sequencer 267
- Output Instruction 267
- Masking Output Data 268
- Chapter 15 273
- Programming the Sequencer 274
- Input Instruction 274
- Sequencer Load Instruction 276
- Load Instruction 276
- File Logic Instructions 280
- FiletoFile AND 281
- FiletoFile OR 283
- FiletoFile XOR 284
- File Complement 285
- WordtoFile Logic 287
- WordtoFile AND 288
- WordtoFile OR 290
- WordtoFile XOR 291
- Chapter 17 294
- File Diagnostics 296
- Troubleshooting Aids 300
- Bit Manipulation and 301
- Bit Manipulation 301
- Bit Monitor 302
- Force On and Force Off 302
- Functions 302
- Forced Address Display 303
- Temporary End Instruction 304
- ERR Message for an Illegal 304
- Chapter 18 305
- Figure 19.1 306
- Edge OneShot 306
- Trailing Edge OneShot 307
- Addressing 308
- 2Slot Addressing 310
- Using 8Point I/O Modules 312
- Using 16Point I/O Modules 313
- Assigning I/O Rack Numbers 314
- 1Slot Addressing 315
- 1/2Slot Addressing 318
- Appendix A 319
- System Configurations 323
- Number Systems 325
- Octal Numbering System 326
- Binary Numbering System 327
- Binary Coded Decimal 328
- Binary Coded Octal 329
- Hexadecimal Numbering 330
- Programming .01Second Timers 332
- Accuracy 333
- 10Msec T 335
- Applications 335
- Appendix C 336
- Scan Time 337
- Program Execution 337
- Compensation 338
- Program ScanTime 340
- Computation 340
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