Number systems
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Transcript of Number systems
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Number systemsMtro. Edgar Sánchez Linares
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A martian problem
When the first Martian to visit Earth attended a high school algebra class, he watched the teacher show that the only solution of the equation 5x2-50x+125=0 is x=5.“How strange”, thougth the Martian. “On Mars, x=5 is a solution of this equation, but there is also another solution.”If Martians have more fingers than humans have, how many fingers do Martians have?
Bonnie Averbach & Orin Chein
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First review – Positional notation
Ten symbols are required by our number system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
The relative position to the decimal point indicates the “place value” of the digit
3= 3x1 =3x100
30= 3x10 =3x101
300= 3x100 =3x102
0.3= 3 /10 =3x10-1
24=
204=
315=
45.2=
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First review – Other bases
What if we have a number system with only two different symbols?
0, 1So, the number 1101 in base two
represents:1 x23 +
How many symbols do we need in base three? And the number 120 represents …
(110)two=
(110)three=
(110)ten=
(110)four=
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First review – Changing bases
(201)three=2x32+0x3+1=(19)ten
(1101)two=(1001)seven=(3.5)six=(T81)eleven=(5403)six=
(10011)two=
=(19)ten
(185)ten=(???)three
= 2 x 81 + (185-162)= 2 x 81 + 23= 2 x 81 + 2 x 9 +(23-18)= 2 x 81 + 2 x 9 + 5= 2 x 81 + 2 x 9 + 3 +2= 2 x 34 + 0 x 33 + +2 x 32+ 1 x 31 + 2 x 30
= (20212)three
Convert (2087)ten into each of the following bases: 2, 3, 6, 7, 12
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Second review - Additionin otherbases