Number systemsMtro. Edgar Sánchez Linares

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

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=

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=

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

Second review - Additionin otherbases