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Digital Logic & Design Lecture No. 3

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Number System Conversion Conversion between binary and octal can be carried out by inspection. Each octal digit corresponds to 3 bits 101 110 010. 011 001 2 = 5 6 2. 3 1 8 010 011 100. 101 001 2 = 2 3 4. 5 1 8 7 4 5. 3 2 8 = 111 100 101. 011 010 2 3 0 6. 0 5 8 = 011 000 110. 000 101 2 Is the number 392.24 8 a valid octal number? 2

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Number System Conversion Conversion between binary and hexadecimal can be carried out by inspection. Each hexadecimal digit corresponds to 4 bits 1001 1010 0110. 1011 0101 2 = 9 A 6. B 5 16 1100 1011 1000. 1110 0111 2 = C B 8. E 7 16 E 9 4. D 2 16 = 1110 1001 0100. 1101 0010 2 1 C 7. 8 F 16 = 0001 1100 0111. 1000 1111 2 Note that the hexadecimal number system requires additional characters to represent its 16 values. 3

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Number Systems 4

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5 Basic Binary Arithmetic

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6 Binary Addition

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7 00 11 + 0 +1 01 1 10 Sum Carry Sum

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Binary Addition 8 Examples: 01011011 +01110010 11001101 00111100 +10101010 10110101 +01101100

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Basic Binary Arithmetic 9 Binary Subtraction

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10 0 10 11 - 0 -1 01 1 0 Difference Borrow

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Binary Subtraction 11 Examples: 01110101 -00110010 01000011 00111100 -10101100 10110001 -01101100

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