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# Lecture 5

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### Lecture 5

1. 1. Data Representation 1 Lecture 5 CSE 211, Computer Organization and Architecture Harjeet Kaur, CSE/IT Overview  Introduction  Data representation  Fixed Point Representation Integer Representation  Floating Point Representation Normalization
2. 2. Data Representation 2 Lecture 5 CSE 211, Computer Organization and Architecture Harjeet Kaur, CSE/IT 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
3. 3. Data Representation 3 Lecture 5 CSE 211, Computer Organization and Architecture Harjeet Kaur, CSE/IT Floating Point Representation Mantissa 0 .1234567 0 04 sign 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. ExponentSign or Example
4. 4. Data Representation 4 Lecture 5 CSE 211, Computer Organization and Architecture Harjeet Kaur, CSE/IT 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