EE101Lecture4

EE101Lecture4 - © Mark Redekopp All rights reserved...

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Unformatted text preview: © Mark Redekopp, All rights reserved Lecture 4 Slides Sign Extension Overflow Binary Logic © Mark Redekopp, All rights reserved 2’s Complement Tricks • Normal method of taking the 2’s complement : – Flip bits and add 1 • Trick – Start from LSB and work your way left towards MSB – Copy bits through the first ‘1’ you encounter – Flip every bit after that 011010 Start from the LSB Copy bits through the first ‘1’ Flip (invert) every bit after that 100110 011010 100101 + 1 100110 Normal 2’s complement method 2’s Complement Trick © Mark Redekopp, All rights reserved Zero and Sign Extension • Zero extension (unsigned) and Sign extension (2’s comp.) is the process of increasing the number of bits used to represent a value without changing the value itself 2’s complement = Sign Extension (Replicate sign bit): Unsigned = Zero Extension (Always add leading 0’s): 111011 = 00 111011 011010 = 00 011010 110011 = 11 110011 pos. neg. Increase a 6-bit number to 8-bit number by zero extending Sign bit is just repeated as many times as necessary © Mark Redekopp, All rights reserved Zero and Sign Truncation • Zero truncation (unsigned) and Sign truncation (2’s comp.) is the process of decreasing the number of bits used to represent a value without changing the value itself 2’s complement = Sign Truncation (Remove copies of sign bit): Unsigned = Zero Truncation (Remove leading 0’s): 00111011 = 111011 00 11010 = 011010 111 1 0011 = 10011 pos. neg. Decrease an 8-bit number to 6-bit number by truncating 0’s. Can’t remove a ‘1’ because value is changed Any copies of the MSB can be removed without changing the numbers value. Be careful not to change the sign by cutting off ALL the sign bits. © Mark Redekopp, All rights reserved Overflow • Overflow occurs when the result of an arithmetic operation is too large to be represented with the given number of bits – Unsigned overflow occurs when adding or subtracting unsigned numbers – Signed (2’s complement overflow) overflow occurs when adding or subtracting 2’s complement numbers © Mark Redekopp, All rights reserved...
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This note was uploaded on 05/13/2008 for the course EE 101 taught by Professor Redekopp during the Fall '06 term at USC.

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EE101Lecture4 - © Mark Redekopp All rights reserved...

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