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# Number system

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DSP integrated circuits

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### Number system

1. 1. NUMBER SYSTEM • CONVENTIONAL NUMBER SYSTEM • REDUNDANT NUMBER SYSTEM • RESIDUE NUMBER SYSTEM
2. 2. CONVENTIONAL NUMBER SYSTEM • It is non-redundant,weighted,positonal number system • Every number x represented as wd-word length wi-weight associated with each digit Positional number system wi depends on the position of the digit xi. Conventional number system wi = xi ,such systems are called fixed-radix systems.
3. 3. Number Integer Fractional part. • A fixed –point number is written from L to R with MSB at L and LSB at R. • 2 distinct forms of fixed-point arithmetic Integer arithmetic ( RH imprtant) (RH kept RH arithmetic dropped) Fractional fixed point (LH imprtnt) (LH kept RH dropped)
4. 4. • Fractional fixed point arithmetic- signed mantissa and exponent. • Advantage-suppress parasitic oscillation , less chip area & faster. Fixed point represented by: • • • • • SIGNED –MAGNITUDE REPRESENTATION COMPLENENT REPRESENTATION ONE’S COMPLENENT REPRESENTATION TWO’S COMPLENENT REPRESENTATION BINARY OFFSET REPRENSATION
5. 5. SIGNED-MAGNITUDE REPRESENTATION • Magnitude & sign represented separately • 1st digit-sign,remaining digit-Magnitude • Representation: • Zero +0 or -0 , not in the case of 1. • Adv : Mul , div easy • Disadv : add,sub – sign-operands
6. 6. COMPLENENT REPRESENTATION • Pos no. – 1’s ,2’s,binary offset = signed mag rep • Neg no. -x=R-x • For y>x x+(R-y)=R-(y-x) • For x>y R-(y-x)=R-(x-y)