Answer:
g
Step-by-step explanation:
a) A good method to convert a decimal number to binary is dividing it by 2 and using the remainder of the division as the converted number, starting by the most significant bit (the right one). We we can't divide anymore. So we have:
217/2 = 108 + 1
108/2 = 54 + 0
54/2 = 27 + 0
27/2 = 13 + 1
13/2 = 6 + 1
6/2 = 3 + 0
3/2 = 2 +1
2/2 = 1
The binary equivalent to 217 is 11011001
b) To convert a number from decimal to hex we can divide the number by 16, taking out the decimal part and multiplying it by 16 using that as our most significant number while using the result of the original division to continue our conversion. So we have:
99/16 = 6.1875
The decimal part is 0.1875, we multiply it by 16 and obtain 3 as our most significant number. Since we can't divide 6 by 16 we have that as our least significant number then the hexadecimal equivalent is 63.
c) We follow the same steps as in item b:
344/16 = 21.5
The most significant number is 0.5*16 = 8
21/16 = 1.3125
The next number is 0.3125*16 = 5
Since we can't divide it anymore we have our result wich is 158 in hex.
d) To convert from decimal to base 7 we'll use the same method as to hex, but this time dividing and multiplying by 7.
136/7 = 19.428571
The most significant number is 0.428571 * 7 = 3
19/7 = 2.71428571
The next number is 0.71428571*7 = 5
Since we can't divide it anymore we have our result wich is 253.
e) To convert from decimal to a base 5 we'll use the same method as before but dividing and multiplying by 5.
542/5 = 108.4
The most significant number is 0.4*5 = 2
108/5 = 21.6
The next number is 0.6*5 = 3
21/5 = 4.2
The next number is 0.2*5 = 1
Since we can't divide it anymore we have our result that is 4132.
f) To convert from decimal to a base 8 we'll use the same method as before but dividing and multiplying by 8.
727/8 = 90.875
The most significant number is 0.875*8 = 7
90/8 = 11.25
The next number is 0.25*8 = 2
11/8 = 1.375
The next number is 0.375*8 = 3
Since we can't divide anymore we have our result wich is 1327
g) Following the same steps as before:
171/16 = 10.6875
The most significant number is 0.6875*16 = 11
Since we can't divide anymore we have our result wich is 1011
h) Following the same steps as before:
91/3 = 30.333333333
The most significant number is 0.333333*3 = 1
30/3 = 10
The next number is 0
10/3 = 3.3333333333
The next number is 0.333333*3 = 1
3/3 = 1
Since we have the final value remainder as 0 the least significant number is 1
Since we can't divide anymore we have our result that is 10101.
i) Following the same steps as before:
840/9 = 93.333333
The most significant number is 0.33333*9 = 3
93/9 = 10.3333333
The next number is 0.333333*9 = 3
10/9 = 1.11111111
The next number is 0.11111111*9 = 1
Since we cant divide anymore we have our result that is 1133
