Lec10_0214

Lec10_0214 - Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W05 L10.1...

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Unformatted text preview: Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W05 L10.1 CS M51A/EE M16 Winter05 Section 1 Logic Design of Digital Systems Lecture 10 Yutao He yutao@cs.ucla.edu 4532B Boelter Hall http://courseweb.seas.ucla.edu/classView.php?term=05W&srs=187154200 February 14 W 0 5 Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W05 L10.2 Outline Administrative Matters Arithmetic Operations Overflow Detection Multiplication Division Arithmetic modules 1-bit half adder 1-bit full adder n-bit full adder * carry-ripple adder ALUs Multipliers Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W05 L10.3 Administrative Matters Project #1 Is posted Midterm Review I will be holding the Midterm Review Session on Wednesday Midterm on Friday Details will be given on Wednesday Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W05 L10.4 Arithmetic - What You Have to Learn Arithmetic o o Signed Integer T.C. Form Positive True Negative Complement Conversion Addition Addition (Carry) Subtraction Complementation + Addition Multiplication Division Shift Left Right Out of Range Overflow . Range Extension . Detection Operation Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W05 L10.5 Overflow Detection Numbers can be represented in computers are limited 32-bits => over 4 billions unique numbers An Overflow occurs when an arithmetic operation results in a number outside the range of those that can be represented Addition Subtraction Multiplication It is desirable to detection the occurrence of an overflow It depends on number systems that are used Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W05 L10.6 Overflow Detection (Contd) Add two positive numbers to get a negative number or two negative numbers to get a positive number 5 + 3 = -8-7 - 2 = +7 0000 0001 0010 0011 1000 0101 0110 0100 1001 1010 1011 1100 1101 0111 1110 1111 +0 +1 +2 +3 +4 +5 +6 +7-8-7-6-5-4-3-2-1 0000 0001 0010 0011 1000 0101 0110 0100 1001 1010 1011 1100 1101 0111 1110 1111 +0 +1 +2 +3 +4 +5 +6 +7-8-7-6-5-4-3-2-1 Y. He @ 02/14/11Y....
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This note was uploaded on 02/14/2011 for the course CS M51A taught by Professor Ercegovac during the Winter '07 term at UCLA.

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Lec10_0214 - Y. He @ 02/14/11 CSM51A/EEM16-Sec.1 W05 L10.1...

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