17 - EE200 DIGITAL LOGIC CIRCUIT DESIGN Class Notes CLASS...

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EE200(class 8-1) Prof. M.M. Dawoud 72 EE200 DIGITAL LOGIC CIRCUIT DESIGN Class Notes CLASS 8-1 The material covered in this class will be as follows: Overflow. BCD adder. Binary multiplier. Magnitude comparator. Overflow Overflow is defined as the situation when two N-digit numbers are added and the sum occupies (N+1) digits. This situation occurs when adding binary numbers as follows: 1. An end carry is generated when adding two N-bit unsigned numbers. 2. The carry-in and carry-out bits are different when adding two N-bit signed binary numbers. Example: Suppose we are adding +70 and +80 using 8-bits in signed 2’s complement form. +70 Æ 01000110 and +80 Æ 01010000 The carry 0 1 +70 0 1 0 0 0 1 1 0 +80 0 1 0 1 0 0 0 0 +150 1 0 0 1 0 1 1 0
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EE200(class 8-1) Prof. M.M. Dawoud 73 The same overflow occurs when adding (-70) + (-80) The carry 1 0 -70 1 0 1 1 1 0 1 0 -80 1 0 1 1 0 0 0 0 -150 0 1 1 0 1 0 1 0 An overflow can be detected by observing the carry-in and the carry-out of the sign bit. If we apply them to an exclusive-or gate then the output is one when overflow occurs.
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17 - EE200 DIGITAL LOGIC CIRCUIT DESIGN Class Notes CLASS...

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