MGMT 1030 Chapter Notes - Chapter 20: Radix Point, Modular Arithmetic, Negative Number
6 May 2018
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MGMT 1030 Chapter 20 Notes – Summary
Introduction
• Tes opleet ad s opleet split the rage siilarly, ut use a sigle alue
for zero.
• This requires the use of a complement based on a value one larger than the largest
number in the base for the given number of digits.
• This ase alue ill alays osist of a folloed y N zeros, here N is the uer
of digits being used.
• Complementation may be taken by inverting the number as before, and adding 1 to the
result, or by subtracting the number from the base value.
• Calculation is straightforward, using modulo arithmetic.
• Most oputer aritheti istrutios are ased o s opleent arithmetic.
• Both s ad s opleet represetatios hae the additioal oeiee that the
sign of a number may be readily identified
• Sie a egatie uer alays egis ith a .
• Small negative numbers have large values, and vice versa.
• Complementary representations for other even-numbered bases can be built similarly.
• Numbers with a fractional part and numbers that are too large to fit within the
constraints of the integer data capacity are stored
• Manipulated in the computer as real, or floating point, numbers.
• In effect, there is a trade-off between accuracy and range of acceptable numbers.
• The usual floating point number format consists of a sign bit, an exponent, and a
mantissa.
• The sign and value of the exponent are usually represented in an excess-N format.
• The base of the exponent is 2 for most systems, but some systems use a different base
for the exponent.
• The radix point is implied.
• When possible, the mantissa is normalized.
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