MGMT 1000 Lecture 5: MGMT 1000 Lecture 5 Notes
MGMT 1000 Lecture 5 Notes – Counting Cycles
Introduction
• As we move leftward to the next digit, that is, the hundreds place, we are now counting
cycles of the rightmost two digits or, in other words, groups of 10×10, or 102, or
hundreds.
• Thus, the number 527 really represents five groups of (10 × 10) + two groups of 10 + 7
• This is also represented as 5 × 102 + 2 × 101 + 7 × 100
• This method can, of course, be extended indefinitely.
• The same method, exactly, applies to any number base.
• The only change is the size of each grouping.
• For example, in base 8, there are only eight different digits available (0, 1, 2, 3, 4, 5, 6,
7).
• Thus, each move left represents eight of the next rightmost grouping.
• The number 6248 corresponds to 6 × 82 + 2 × 81 + 4 × 80
• Since 82 =6410, 81 =810, and 80 =1, 6248=6×64+2×8+4=40410
• Each digit in a number has a weight, or importance, relative to its neighbors left and
right.
• The weight of a particular digit in a number is the multiplication factor used to
determine the overall value of the particular digit.
• For example, the weights of the digits in base 8, reading from right to left are 1, 8, 64,
256, or, if you prefer, 80, 81, 82, 83
• Just as you would expect, the weight of a digit in any base n is n times as large as the
digit to its right and (1/n)th as large as the digit to its left.
• The corresponding method of counting in base 2.
• Note that each digit has twice the weight of its next rightmost neighbor
• Just as in base 10 each digit had ten times the weight of its right neighbor.
• This is what you would expect if you consider that there are only two different values
for digits in the binary cycle.
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