This document discusses number systems and bases. It begins by describing a "Martian problem" where Martians have a different number system than humans. It then discusses how: 1) Positional notation uses the position of digits to indicate place value, allowing more numbers to be represented with fewer symbols. 2) Different number bases use different sets of symbols, affecting how numbers are represented. For example, in base 2 only 0 and 1 are used. 3) Converting between number bases involves determining the place value of each digit in the new base. For example, (201)three = (19)ten as 2*32 + 0*3 + 1 in base 3 equals 19 in base 10.

1. NumbersystemsMtro. Edgar Sánchez Linares

2. A martianproblemWhenthefirstMartiantovisitEarthattended a highschool algebra class, he watchedtheteacher show thattheonlysolution of theequation5x2-50x+125=0isx=5.“Howstrange”, thougththeMartian. “OnMars, x=5is a solution of thisequation, butthereisalsoanothersolution.”IfMartianshave more fingersthanhumanshave, howmanyfingers do Martianshave?Bonnie Averbach & OrinChein

3. Firstreview – PositionalnotationTen symbols are required by our number system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 924=204=315=45.2=The relative position to the decimal point indicates the “place value” of the digit 3= 3x1 =3x100 30= 3x10 =3x101300= 3x100 =3x1020.3= 3 /10 =3x10-1

4. First review – Other basesWhat if we have a number system with only two different symbols? (110)two=(110)three=(110)ten=(110)four=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 …

5. First review – Changing bases(201)three=2x32+0x3+1=(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(10011)two==(19)ten(1101)two=(1001)seven=(3.5)six=(T81)eleven=(5403)six=Convert (2087)teninto each of the following bases: 2, 3, 6, 7, 12

6. Secondreview - Additionin otherbases