MGMT 1000 Lecture Notes - Lecture 7: Calculator
MGMT 1000 Lecture 7 Notes – Preceding Discussion
Introduction
• From the preceding discussion, it is fairly easy to determine the total range of possible
numbers—or, equivalently, the smallest and largest integer—for a given number of
digits in a particular number base.
• Since the weight of each digit is one larger than the largest value that can be
represented by all the digits to its right.
• Then the range of possible values for n digits is simply the weight of the nth digit, which
is represented by the value range = basen
• Thus, if we want to know how many different numbers can be represented by two
decimal digits, the answer is 102.
• We can represent one hundred different numbers (0 . . . 99) with two decimal digits.
• Its oiously easie to siply eoize the foula
• If you are told that you are working with four digit numbers in base 8, you know from
the formula that you can represent 84, or 4096 different numbers, ranging from 0 . . .
77778, or the decimal equivalent (0 . . . 4095).
• Just as a pocket calculator stores, manipulates, and displays numbers as a group of
digits, so computers store and manipulate numbers as groups of bits.
• Most computers work with numbers 16 bits, 32 bits, or 64 bits at a time.
• Applyig the peedig foula to a -it PC, you a epeset =,
different number values in each 16-bit location.
• If you wish to extend this range, it is necessary to use some technique for increasing the
number of bits used to hold your numbers, such as using two 16-bit storage locations
together to hold 32 bits.
• There are other methods used, which are discussed, but note that, regardless of the
technique used, there is no way to store more than 65,536 different number values
using 16 bits.
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