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2-Mod5_LS_2011

# 2-Mod5_LS_2011 - ECE 270 Introduction to Digital System...

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ECE 270 Introduction to Digital System Design © 2011 by D. G. Meyer 1 Lecture Summary – Module 5-A Unsigned Number Base Conversion Reference: Text (4 th Ed.), pp. 25-34; (3 rd Ed.), pp. 25-34 overview o d n – digits of base R number o c n – converted corresponding digits in base 10 o dealing with unsigned numbers only at this point leading zeroes don’t matter o table of correspondence integer conversion: base R to base 10 o method: iterative multiply and add o based on nested expression of a number integer conversion: base 10 to base R o method: iterative division o remainders become digits of converted number o quotient of zero indicates conversion is complete (d 3 d 2 d 1 d 0 ) R = (N) 10 = c 3 xR 3 + c 2 xR 2 + c 1 xR 1 + c 0 xR 0 = (((c 3 x R + c 2 ) x R + c 1 ) x R + c 0 )

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ECE 270 Introduction to Digital System Design © 2011 by D. G. Meyer 2 short cut for conversion among powers of 2 (from base “A” to base “B”) o method: size log 2 R groupings o write an n-digit binary number for each base A digit in the original number, where n = log 2 A o starting at the least significant position, form m-digit groups, where m = log 2 B

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