1. FLOATING-POINT NUMBER REPRESENTATION
Dr. Konstantinos Tatas
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. ACOE161 - Digital Logic for Computers - Frederick University
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
Sign (S)
Biased exponent (E)
Unsigned normalized mantissa (M)
ACOE161 - Digital Logic for Computers - Frederick University

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

6. Examples (IEEE short real format)
Binary
value
Normalized
Binary value
exponent
Biased
Exponent
(Excess -127
Sign, exponent, mantissa
-1.01
127 +3
130
-1.1 -6
121 +7
134
ACOE161 - Digital Logic for Computers - Frederick University

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