722222 1/2 22 -2 = Integer quotient 20 20 = 10 5 = 2 11 = 1 0 + Remainder 12 0 Coefficient 40 = 1 a = 0 0 a = 0 -2 12 a3 = 1 a = 0 as = 1 answer: (41)10 = (asa4a3azaao)2 = (101001) The arithmetic process can be manipulated more conveniently as follows: Integer 41 Remainder 20 10 0 5 0 2 1 0 0 101001 answer The conversion from decimal integers to any base-r system is similar to the exam- ple, except that division is done by r instead of 2. Convert decimal 153 to octal. The required base r is 8. First, 153 is divided by 8 to give an integer quotient of 19 and a remainder of 1. Then 19 is divided by 8 to give an integer quotient of 2 and a remainder of 3. Finally, 2 is divided by 8 to give a quotient of 0 and a remainder of 2. This process can be conveniently manipulated as follows: 153 19 1 2 3 021 = (231)8 Show that the automata M and M defined by Fig. 5.24 are not equivalent. 91 92 (a) d 94 C d 95 96 (b) Fig. 5.24 (a) Automaton M, and (b) automaton M. A Xm Fig. 6.5 Derivation tree for one-step derivation.