Overview Introduction Data representation Fixed Point Representation

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Overview Introduction Data representation Fixed Point Representation Data Representation 1 Lecture 5 Overview Introduction Data representation Fixed Point Representation Integer Representation Floating Point Representation Normalization CSE 211, Computer Organization and Architecture Harjeet Kaur, CSE/IT

Floating Point Representation Data Representation 2 Lecture 5 Floating Point Representation The location of the fractional point is not fixed to a certain location The range of the represent able numbers is wide F = EM mn ekek-1 ... e0 mn-1mn-2 … m0 . m-1 … m-m sign exponent mantissa - Mantissa Signed fixed point number, either an integer or a fractional number - Exponent Designates the position of the radix point Decimal Value V(F) = V(M) * RV(E) V stands for Value M: Mantissa E: Exponent R: Radix CSE 211, Computer Organization and Architecture Harjeet Kaur, CSE/IT

Floating Point Representation Data Representation 3 Lecture 5 Floating Point Representation Example .1234567 04 sign mantissa exponent ==> +.1234567 x 10+04 Example A binary number +1001.11 in 16-bit floating point number representation (6-bit exponent and 10-bit fractional mantissa) 0 000100 100111000 0 000101 010011100 Note: In Floating Point Number representation, only Mantissa(M) and Exponent(E) are explicitly represented. The Radix(R) and the position of the Radix Point are implied. Exponent Sign or Mantissa CSE 211, Computer Organization and Architecture Harjeet Kaur, CSE/IT

Floating Point Representation-Normalization Data Representation 4 Lecture 5 Floating Point Representation-Normalization A Floating Point number is said to be normalized if the most significant digit of the mantissa is nonzero E.g. Binary number 00011010 is not normalized CSE 211, Computer Organization and Architecture Harjeet Kaur, CSE/IT