Page 57 - Cs_withBlue_J_C11_Flipbook
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Thus, a decimal number 12.5 can be represented as:
• 0.00125 × 10 4
• 0.125 × 10 2
3
• 0.0125 × 10 and so on
Here, we see that the exponent changes with the change in mantissa so that the value is not altered. Also, note the
change in the position of the decimal point.
Definition
The floating number representation of a number can implement high range of values. It consists of two parts namely
mantissa and exponent. The mantissa represents a signed fixed point number. The exponent denotes and designates
the position of the decimal (or binary) point.
Normalised Scientific Notation
In this notation, there is a single non-zero digit before the radix point.
2
A decimal number in 238.567 in normalised notation is represented as 2.38567 × 10 .
A binary number 110.011 in normalised notation will be 1.10011 × 2 . Since a binary number contains only 0 and 1, all
2
the numbers will have a single 1 before the radix point in normalised representation.
Mantissa Exponent Notation
Floating point binary numbers are represented as Mantissa × 2 exponent in this notation. Mantissa is represented in
normalised binary form.
Excess Notation
Excess N or biased notation is also used to represent signed floating point numbers. In this notation, a number called
magic number (N) is added to the original number to shift all the values by N. The number represented by this notation
is N less than the unsigned value.
Consider 3-bit numbers
Numbers Binary Excess-4 notation
0 000 0 - 4 = -4
1 001 1 - 4 = -3
2 010 2 - 4 = -2
3 011 3 - 4 = -1
4 100 4 - 4 = 0
5 101 5 - 4 = 1
6 110 6 - 4 = 2
7 111 7 - 4 = 3
According to IEEE (Institute of Electrical and Electronics Engineers), a floating-point number has 3 parts which are as
follows:
• The sign of mantissa: It assumes 0 for a positive number and 1 for negative.
• The biased exponent: A bias (or excess) is added to the actual exponent to represent both positive and negative
exponents.
• The mantissa: It represents the actual digits of floating point numbers. It contains a single leading bit before the radix
point and the fractional bits after the radix point. But the bits to the right of binary points are only stored internally.
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