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

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

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Logic Circuits Course Arab International University Faculty of Informatics and Communication Engineering (FICE) Ch. 2-2 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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7- Arithmetic Operations with Signed Numbers • Addition • Subtraction • Multiplication • Division 3
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4 1- Addition : Add the two numbers and discard any final carry bit as long as 2 nd complement is used for negative numbers. Examples : Addend Augend Sum Four conditions for adding numbers: Both numbers are positive. A positive number that is larger than a negative number. A negative number that is larger than a positive number. Both numbers are negative. +
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5 Add the two numbers and discard any final carry bit as long as 2 nd complement is used for negative numbers. +
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6 Overflow Condition The sum exceeds the number of bits in the two numbers (the sum exceeds 7 bits) An overflow results as indicated by an incorrect sign bit 125 +58 183
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2- Subtraction 1. Take the 2 nd complement of the subtrahend , then add it to the minuend. 2. Discard any final carry bit 7 Subtraction is addition with the sign of the subtrahend changed. Example in Decimal number 30 – 12 = 18 >>>>> 30 + 88 = 118 (88 is the 2 nd complement of 12 ) discard carry = 18 minuend subtrahend difference
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8
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3- Multiplication 1. Determine if the signs of the multiplicand and multiplier are the same or different . Therefore, determine the sign of the product 2. Change any negative number to true form (un-complemented) 3. Generate the partial products , shift each successive partial product one bit to the left. 4. Add each successive partial products to the sum of previous partial product. 5. If the sign bit that was determined in step -1- is negative , take the 2 nd complement of the product.
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Ch. 2-2 Number Systems, Operations, and Codes- - Logic...

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