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# #4 - sign bit Any carry out from the sign bit is ignored No...

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EE200(class 2-1) Prof. M.M. Dawoud 12 EE200 DIGITAL LOGIC CIRCUIT DESIGN Class Notes CLASS 2-3 The material covered in this class will be as follows: Signed binary numbers Addition and Subtraction of Signed binary numbers. Signed Binary Numbers: Unsigned binary numbers Æ ) 1 ( 2 n 0 2 n bit binary number Æ Signed binary numbers Æ Sign bit ) 2 ( 2 n 0 2 The sign bit is 0 for “ + “ and 1 for “ – “. Three types of signed numbers are used Examples using 8 bits 1. Signed magnitude representation +9 Æ 00001001 -9 Æ 10001001 2. Signed 1’s complement representation +9 Æ 00001001 -9 Æ 11110110 3. Signed 2’s complement representation +9 Æ 00001001 -9 Æ 11110111

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EE200(class 2-1) Prof. M.M. Dawoud 13 Addition of signed binary numbers: 1. In signed magnitude representation follow the rules of ordinary arithmetic. If the signs are the same, add the magnitudes and give the sum the same sign. If different signs, subtract and give the result the sign of the big number. 2. In complement representation, add the two numbers including the
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Unformatted text preview: sign bit. Any carry out from the sign bit is ignored. No comparison or subtraction is needed. Examples: Add (-6) + (+13) using signed 2’s complement form with 8 bits. Repeat for (+6) + (-13) Answer Æ 00000110 ) 6 ( ≡ + and 00001101 ) 13 ( ≡ + 11111010 ) 6 ( ≡ − ∴ and 11110011 ) 13 ( ≡ − . -6 Æ 11111010 +13 Æ 00001101 100000111 Æ Answer is +7 Also, +6 Æ 00000110 -13 Æ 11110011 11111001 Æ Answer is – 7 Sign bit Sign bit Carry out EE200(class 2-1) Prof. M.M. Dawoud 14 Arithmetic Subtraction: Take the 2’s complement of the subtrahend, including the sign bit, and add it to the minuend. A carry out is discarded. ) ( ) ( ) ( ) ( B A B A ∓ + ± = ± − ± Example: Perform the subtraction (-6) - (-13) using signed 2’s complement representation with 8 bits. (-6) 11111010 Æ (-6) 11111010 -(-13) 11110011 Æ +(+13) 00001101 100000111 Æ Answer is +7 Carry out Sign bit...
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#4 - sign bit Any carry out from the sign bit is ignored No...

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