Question

1. 15% Give illustrative example(s) of number(s) in number systems with base 20, 02, 11/5 Prove that such examples are valid by translating selected numbers to decimal number system and then back to the required one For example, if you were asked to illustrate number system with base 8 you would write 43g 4x 8 3 x 8° = 3510, so 43g = 3510- Reverse translation can be accomplished by dividing 3510 by 8 and writing down result of the last division followed by all remainders in the reverse order, .e. 3510 = 43g.

Answer 1

In the number system base 20, the numbers 0 to 9 are utilised as it is but 10 to 19 are denoted by capital letters A to J. Thus 7 89 12 13 Decimal(Base 10) 1 2 3 4 5 6 10 11 14 15 16 17 18 19 Vigesimal (Base 20) 01 23 45 67 89 A C D E G Н Any number in base 20 is described as follows: 5 x 2057 X 204 + 8 x 203 + E x 202 + F X 201 + I x 20° 578EFI20 = 5 x 205 7 x 204 + 8 x 203 + 14 x 202 + 15 x 201 + 18 x 20° 1718991810 Power of 20 4 2 1 0 digits Total 7 8 14 15 18 16000000 1120000 64000 5600 300 18 17189918 Thusthe number 578EF120 in base 20 has value 1718991810 in base 10. L LC

wish to convert 17189918,0 into base 20 then we have to do as follows. f we Dividing by Notation in 20 Base 20 Number Remainder Quotient 859495 17189918 18 F 859495 42974 15 E 42974 2148 14 8 2148 107 8 7 107 5 7 5 0 5 Thus 1718991810 becomes 578EF120- For base 02, the digits 0 and 1 are utilized. Thus = 1 x 25 1 x 24 + 1 x 23 + 0 x 22 + 0 x 21 + 1 x 2° 1110012 5710 we wish to convert 5710 into base 2 then we have to do as follows If Dividing by 2 Number Remainder Quotient 57 28 1 28 14 0 14 7 0 7 3 1 1 1 1 0 1 5710 becomes 1110012