MGMT 1000 Lecture Notes - Lecture 20: Radix Point
MGMT 1000 Lecture 20 Notes – Number Point
Introduction
• Moving the point right one space, therefore, multiplies the number by ten.
• Only a bit less obvious (pun intended), 1002 is twice as big as 102
• Note: We hae used the phrase uer poit eause the ord deial
specifically implies base 10.
• More generally, the number point is known by the name of its base, for example, binary
point or hexadecimal point.
• It is sometimes also called a radix point.
• The opposite is also true
• If we move the number point to the left one place, the value is divided by the base.
• Thus, each digit has strength 1/B of its left neighbor.
• This is true on both sides of the number point.
• Moving the point to the left one space divides the value by ten.
• Thus, for numbers to the right of the number point, successive digits have values 1/B,
1/B2, 1/B3, and so on.
• In base 10, the digits then have value.
• .D1 D2 D3 D4 101 102 103 104 which is equivalent to 1/10 1/100 1/1000 1/10, 000
• This should come as no surprise to you, since 1/10=0.1, 1/100=0.01, and so forth.
• ‘eeer fro algera that B−k =1/Bk.
• Then, a decimal number such as 0.2589 has value 2 × (1/10) + 5 × (1/100) + 8 × (1/1000)
+ 9 × (1/10, 000)
• Similarly in base 2, each place to the right of the binary point is 1/2 the weight of its left-
hand neighbor.
• Thus, we have .B1 B2 B3 B4 1/2 1/4 1/8 1/16 etc.
• As an example, 0.101011 is equivalent to 1/2 + 1/8 + 1/32 + 1/64 which has decimal
value 0.5 + 0.125 + 0.03125 + 0.015625 = 0.67187510
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