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Prepared By:
S.Visnu Dharsini
Assistant Professor-CSE
IEEE 754
 It is not represented by
85.236
56620.856647783
 It is represented by
1.101101*2^6
0.001011011*2^9 Exponent
Both of this in
Normalized form
 Sign
 Exponent
 Mantissa
 Sign is
101110110First bit is the sign bit in Binary (0+ve) (1-ve)
 Exponent is derived from 2 formulas
 Mantissa is also derived from this 2 formulas
Single Precision Double Precision
(1.N)2E-
127
(1.N)2E-
1023
Comparison
should be
made to get
E
N is the Mantissa part
 Addition
 Subtraction
 Multiplication
 Division
Add (1.1100*24) + (1.100*22)
Sol:- Make the Exponent equal like
(1.1100*24) + (0.01100*24)
Now ADD the Digit
1.1100 *24
+ 0.0110 *24
10.0010 *24
Now Normalize the result like:
10.0010*24 0.100010 *26 (Ans)
Add (1.1100*24) + (1.100*22)
Sol:- Make the Exponent equal like
(1.1100*24) - (0.01100*24)
Now ADD the Digit
1.1100 *24
- 0.0110 *24
1.0110 *24
Now Normalize the result like:
1.0110*24 (Ans)

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Floating point representation

  • 3.  It is not represented by 85.236 56620.856647783  It is represented by 1.101101*2^6 0.001011011*2^9 Exponent Both of this in Normalized form
  • 4.
  • 5.  Sign  Exponent  Mantissa  Sign is 101110110First bit is the sign bit in Binary (0+ve) (1-ve)  Exponent is derived from 2 formulas  Mantissa is also derived from this 2 formulas Single Precision Double Precision (1.N)2E- 127 (1.N)2E- 1023 Comparison should be made to get E N is the Mantissa part
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.  Addition  Subtraction  Multiplication  Division
  • 13. Add (1.1100*24) + (1.100*22) Sol:- Make the Exponent equal like (1.1100*24) + (0.01100*24) Now ADD the Digit 1.1100 *24 + 0.0110 *24 10.0010 *24 Now Normalize the result like: 10.0010*24 0.100010 *26 (Ans)
  • 14. Add (1.1100*24) + (1.100*22) Sol:- Make the Exponent equal like (1.1100*24) - (0.01100*24) Now ADD the Digit 1.1100 *24 - 0.0110 *24 1.0110 *24 Now Normalize the result like: 1.0110*24 (Ans)