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Dr. Konstantinos Tatas

Dr. Konstantinos Tatas

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Dr. Konstantinos Tatas

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  1. Dr. Konstantinos Tatas FLOATING-POINT NUMBER REPRESENTATION ACOE161 - Digital Logic for Computers - Frederick University

  2. The range/accuracy problem • The range of numbers that can be represented with n bits is • In 2’s complement: from - /2 to /2 -1 • For n=8: From –128 to +127 • For n=16: From –32,768 to +32,767 • Still, in many application an even larger range is required ACOE161 - Digital Logic for Computers - Frederick University

  3. Real numbers • Instead of representing the actual value, in the base system, we represent the sign, M, b and e ACOE161 - Digital Logic for Computers - Frederick University

  4. FLOATING-POINT REPRESENTATION • IEEE short real: 8 bits for the exponent (in Ex-127), 23 bits for the mantissa • IEEE long real: 11 bits for the exponent, 52 bits for the mantissa ACOE161 - Digital Logic for Computers - Frederick University

  5. RESERVED VALUES ACOE161 - Digital Logic for Computers - Frederick University

  6. Examples (IEEE short real format) ACOE161 - Digital Logic for Computers - Frederick University

  7. Homework • Convert the following 2’s complement values to IEEE short real floating-point representation • 10011010 • 0110.0101 • 0.1111110 • 1100.0001 ACOE161 - Digital Logic for Computers - Frederick University