MGMT 1030 Chapter 13: MGMT 1030 Chapter 13 Notes
6 May 2018
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MGMT 1030 Chapter 13 Notes – Summary
Introduction
• Here are some examples of binary floating point format using this notation.
• Again we have assumed that the binary point is at the start of the mantissa.
• The base of the exponent is 2.
• Thanks to the nature of the binary system, the 23 bits of mantissa can be stretched to
provide 24 bits of precision, which corresponds to approximately seven decimal digits of
precision.
• Sie the leadig it of the atissa ust e if the ue is normalized, there is
no need to store the most significant bit explicitly.
• Instead, the leading bit can be treated implicitly, similar to the binary point.
• There are three potential disadvantages to using this trick.
• First, the assumption that the leadig it is always a eas that we aot stoe
numbers too small to be normalized, which slightly limits the small end of the range.
• Seod, ay foat that ay euie a i the ost sigifiat it fo ay easo
cannot use this method.
• Finally, this method requires that we provide a separate way to store the number 0.0,
sie the euieet that the leadig it e a akes a atissa of . a
impossibility!
• Since the additional bit doubles the available precision of the mantissa in all numbers,
the slightly narrowed range is usually considered an acceptable trade-off.
• The number 0.0 is handled by selecting a particular 32-bit word and assigning it the
value 0.0.
• Twenty-four bits of mantissa corresponds to approximately seven decimal digits of
precision.
• Dot foget that the ase ad iplied iay poit ust also e speified.
• There are many variations, providing different degrees of precision and exponential
range
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