Ch. 2-1 Number Systems, Operations, and Codes

Ch. 2-1 Number Systems, Operations, and Codes - Logic...

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Logic Circuits Course Arab International University Faculty of Informatics and Communication Engineering (FICE) Ch. 2-1 Number Systems Operations and Codes Dr. Marwan Zabibi
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2 1. Decimal Numbers 2. Binary Numbers 3. Decimal to Binary Conversion 4. Binary Arithmetic 5. 1 st and 2 nd Complement of Binary Numbers 6. Signed Numbers 7. Arithmetic Operation with Signed Numbers 8. Hexadecimal Numbers 9. Octal Numbers 10. Binary Coded Decimal (BCD) 11. Digital Codes 12. Error Detecting Codes Contents
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1-Decimal Numbers 4 The decimal number system has ten digits . These are : 0 , 1 , 2 , 3, 4 , 5 , 6 , 7 , 8 , 9 . The decimal number system has the base = 10 Example -1- Example -2-
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2- Binary Numbers • The binary number system has two digits: 0 and 1 • The binary numbering system has a base of 2 with each position weighted by a factor of 2: 5
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Binary Numbers 2 bits 3 bits 4 bits 5 bits 8 bits word (byte) 0 00 000 0000 00000 00000000 1 01 001 0001 00001 00000001 2 10 010 0010 00010 00000010 3 11 011 0011 4 100 0100 5 101 0101 6 110 0110 7 111 0111 8 1000 9 1001 10 1010 01010 00001010 2 bits word represents 4 different codes 2 2 =4 3 bits word gives 2 3 =8 codes 4 bits word gives 2 4 =16 codes 8 bits word (byte) gives 2 8 =256 codes, n bits word, 2 n codes
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Digital Codes: Alphanumeric codes 6 Alphanumeric codes are codes that represent alphabetic characters (letters ), and numbers. Most such codes also represent symbols and control characters necessary to conveying information. In 1981, IBM introduced extended ASCII, which is an 8-bit code and increased the character set to 256. In its original form, ASCII encoded 128 characters and symbols using 7- bits. The first 32 characters are control characters, that are based on obsolete teletype requirements, so these characters are generally assigned to other functions in modern usage. Other extended sets (such as Unicode ) have been introduced to handle characters in languages other than English. ASCII Code: American Standard Code for Information Interchange
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Digital Codes • ASCII code (control characters) 7
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Digital Codes • ASCII code (graphic symbols 20h – 3Fh)
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Digital Codes • ASCII code (graphic symbols 40h – 5Fh)
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Digital Codes • ASCII code (graphic symbols 60h – 7Fh)
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This note was uploaded on 03/12/2012 for the course IT 101 taught by Professor Fadi during the Spring '12 term at University of Damascus.

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Ch. 2-1 Number Systems, Operations, and Codes - Logic...

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