Consider the poset .Z; / (ordinary less than or equal to). For x; y 2 Z, explain in

Math 116: Base systems contd. Convert 5342 in6o a base 10: 56 +36 +46 +26 ( you expand the # and multiply by base 6) 5216+336+46+21 (exponent goes from last base # to first base # from 0-3) 1080+108+24+2=1214 convert 245 to a base 5: (when you go from base 10 to a smaller base divide) 0 5 =1 (put a 0 for numbers skipped) 5 =5 20/5 (4 remainder) 45=20 20-20=0 2 5 =25 120/25 (4 remainder) 425= 100 120-100=20 3 5 =125 245/125 (1 remainder) 1251=125 245-125=120 *you multiply the remainder and the number divided in order to get the next number. 15 +45 +45 +05 = 1440 5 convert 3324 to5a base 6 (convert b4 to a b10 # then convert to b6#) 3 2 1 0 35 +35 +25 +45 3125+325+25+41 375+75+10+4+ 464 base 6 0 6 =1 2/1 (2 remainder) 21=2 2-2=0 6 =6 32/6 (5 remainder) 65=30 32-30=2 2 6 =36 (put a 0 for numbers skipped) 6 =216 464/216 (2 remainder) 2216=432 464-432=32 26 +06 +56 +26 = 2052 6 Prime Numbers: a prime number is a number that can only be divided by 1 and itself Examples for prime numbers: 1, 2, 3, 5, 7, 11, 13, 17. Composite number: has factors other than 1 and itself Examples of composite numbers: 16, 20, 25. Number Divisibility test for number 2 Number is even 3 Sum of the digits of the number is 3 4 The last two digits of number are divisible by 4 5 The number ends in 0 or 5