MGMT 1000 Lecture Notes - Lecture 6: Binary Number
MGMT 1000 Lecture 6 Notes – Studying the Table
Introduction
• You should spend enough time studying this table until you understand every detail
thoroughly.
• Note, too, that the steps that we have followed do not really depend on the number
base that we are using.
• We simply go through a complete cycle, exhausting all possible different digits in the
base set, and then move to the left one place and count the cycles.
• We repeat this process as necessary to represent the entire number.
• In general, for any number base B, each digit position represents B to a power, where
the power is numbered from the rightmost digit, starting with B0.
• B0, of course, is one (known as the units place) for any number base.
• Thus, a simple way to determine the decimal equivalent for a number in any number
base is to multiply each digit by the weight in the given base that corresponds to the
position of the digit for that number.
• Often it is useful to be able to estimate quickly the value of a binary number.
• Since the weight of each place in a binary number doubles as we move to the left
• We can generate a rough order-of-magnitude by considering only the weight for the
leftmost bit or two.
• Starting from 1 and doubling for each bit in the number to get the weight, you can see
that the most significant bit in the previous example has a value of 256.
• We can improve the estimate by adding half that again for the next most significant bit,
which gives the value of the number in the neighborhood of 384, plus a little more for
the additional bits.
• With a little practice, it is easy to estimate the magnitudes of binary numbers almost
instantly.
• This technique is often sufficient for checking the results of calculations when debugging
programs.
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