ANSWERS to selected problems
on
base number systems homework
( 1)
decimal place values: 1, 10, 100, 1000
base-5 place values: 1, 5, 25, 125
octal place values: 1, 8, 64, 512
hexadecimal place values: 1, 16, 256, 4096
Mayan place values: 1, 20, 400, 8000
Babylonian place values: 1, 60, 3600, 216000
binary place values: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
( 2)
7; 517
194; 61,725
17; 167
350; 2498
360; 6543
( 3) 123 (base 5); 1314 (base 5)
( 4) 1:25; 5:32:47
( 5)
6 17; 3 0 15; 1 1 12 1 19 9
or in Mayan symbols...
( 6) 10110111 (bin); 110011010 (bin)
( 7) 21 (oct); 3661 (oct)
( 8)
18
50
99, 100, 101
80, 79, 78
29, 28, 27
( 9)
24 (base 5)
20 (base 5)
44 (base 5), 100 (base 5), 101 (base 5)
40 (base 5), 34 (base 5), 33 (base 5)
144 (base 5), 143 (base 5), 142 (base 5)
(10)
53 (base 8)
40 (base 8)
77 (base 8), 100 (base 8), 101 (base 8)
60 (base 8), 57 (base 8), 56 (base 8)
477 (base 8), 476 (base 8), 475 (base 8)
(11)
1:08 (base 60)
18:00 (base 60)
59:59 (base 60), 1:00:00 (base 60), 1:00:01 (base 60)
24:00 (base 60), 23:59 (base 60), 23:58 (base 60)
2:59:59 (base 60), 2:59:58 (base 60), 2:59:57 (base 60)
(12)
11 (bin)
110 (bin)
111 (bin), 1000 (bin), 1001 (bin)
1000 (bin), 111 (bin), 110 (bin)
1011 (bin), 1010 (bin), 1001 (bin)
(13)
(14)
1 (bin) "one"
10 (bin) "two"
11 (bin) "three"
100 (bin) "four"
101 (bin) "five"
110 (bin) "six"
111 (bin) "seven"
1000 (bin) "eight"
1001 (bin) "nine"
1010 (bin) "ten"
1011 (bin) "eleven"
1100 (bin) "twelve"
1101 (bin) "thirteen"
1110 (bin) "fourteen"
1111 (bin) "fifteen"
10000 (bin) "sixteen"
10001 (bin) "seventeen"
10010 (bin) "eighteen"
10011 (bin) "nineteen"
10100 (bin) "twenty"
10101 (bin) "twenty-one"
10110 (bin) "twenty-two"
10111 (bin) "twenty-three"
11000 (bin) "twenty-four"
11001 (bin) "twenty-five"
11010 (bin) "twenty-six"
11011 (bin) "twenty-seven"
11100 (bin) "twenty-eight"
11101 (bin) "twenty-nine"
11110 (bin) "thirty"
11111 (bin) "thirty-one"
100000 (bin) "thirty-two"
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