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Contents
Review Questions
17
Problems
17
Further Reading
18
2 Binary Codes
19
2.1 Binary Coded Decimal
19
2.1.1 BCD-to-Binary Conversion
20
2.1.2 Binary-to-BCD Conversion
20
2.1.3 Higher-Density BCD Encoding
21
2.1.4 Packed and Unpacked BCD Numbers
21
2.2 Excess-3 Code
21
2.3 Gray Code
23
2.3.1 Binary–Gray Code Conversion
24
2.3.2 Gray Code–Binary Conversion
25
2.3.3 n-ary Gray Code
25
2.3.4 Applications
25
2.4 Alphanumeric Codes
27
2.4.1 ASCII code
28
2.4.2 EBCDIC code
31
2.4.3 Unicode
37
2.5 Seven-segment Display Code
38
2.6 Error Detection and Correction Codes
40
2.6.1 Parity Code
41
2.6.2 Repetition Code
41
2.6.3 Cyclic Redundancy Check Code
41
2.6.4 Hamming Code
42
Review Questions
44
Problems
45
Further Reading
45
3 Digital Arithmetic
47
3.1 Basic Rules of Binary Addition and Subtraction
47
3.2 Addition of Larger-Bit Binary Numbers
49
3.2.1 Addition Using the 2’s Complement Method
49
3.3 Subtraction of Larger-Bit Binary Numbers
52
3.3.1 Subtraction Using 2’s Complement Arithmetic
53
3.4 BCD Addition and Subtraction in Excess-3 Code
57
3.4.1 Addition
57
3.4.2 Subtraction
57
3.5 Binary Multiplication
58
3.5.1 Repeated Left-Shift and Add Algorithm
59
3.5.2 Repeated Add and Right-Shift Algorithm
59
3.6 Binary Division
60
3.6.1 Repeated Right-Shift and Subtract Algorithm
61
3.6.2 Repeated Subtract and Left-Shift Algorithm
62
3.7 Floating-Point Arithmetic
64
3.7.1 Addition and Subtraction
65
3.7.2 Multiplication and Division
65