Contents
xi
6.3.8 Theorem 8
196
6.3.9 Theorem 9
197
6.3.10 Theorem 10 (Absorption Law or Redundancy Law)
197
6.3.11 Theorem 11
197
6.3.12 Theorem 12 (Consensus Theorem)
198
6.3.13 Theorem 13 (DeMorgan’s Theorem)
199
6.3.14 Theorem 14 (Transposition Theorem)
200
6.3.15 Theorem 15
201
6.3.16 Theorem 16
201
6.3.17 Theorem 17 (Involution Law)
202
6.4 Simplification Techniques
204
6.4.1 Sum-of-Products Boolean Expressions
204
6.4.2 Product-of-Sums Expressions
205
6.4.3 Expanded Forms of Boolean Expressions
206
6.4.4 Canonical Form of Boolean Expressions
206
6.4.5 and Nomenclature
207
6.5 Quine–McCluskey Tabular Method
208
6.5.1 Tabular Method for Multi-Output Functions
212
6.6 Karnaugh Map Method
216
6.6.1 Construction of a Karnaugh Map
216
6.6.2 Karnaugh Map for Boolean Expressions with a Larger Number of
Variables
222
6.6.3 Karnaugh Maps for Multi-Output Functions
225
Review Questions
230
Problems
230
Further Reading
231
7 Arithmetic Circuits
233
7.1 Combinational Circuits
233
7.2 Implementing Combinational Logic
235
7.3 Arithmetic Circuits – Basic Building Blocks
236
7.3.1 Half-Adder
236
7.3.2 Full Adder
237
7.3.3 Half-Subtractor
240
7.3.4 Full Subtractor
242
7.3.5 Controlled Inverter
244
7.4 Adder–Subtractor
245
7.5 BCD Adder
246
7.6 Carry Propagation–Look-Ahead Carry Generator
254
7.7 Arithmetic Logic Unit (ALU)
260
7.8 Multipliers
260
7.9 Magnitude Comparator
261
7.9.1 Cascading Magnitude Comparators
263
7.10 Application-Relevant Information
266
Review Questions
266
Problems
267
Further Reading
268