convert 736 into quinary system
Answers
Answer:
In numeral system, we know hexadecimal is base-16 and quinary is base-5. To convert hexadecimal 736B.6 to quinary, you follow these steps:
To do this, first convert hexadecimal into decimal, then the resulting decimal into quinary
Start from one's place in hexadecimal : multiply ones place with 16^0, tens place with 16^1, hundreds place with 16^2 and so on from right to left
Add all the products we got from step 1 to get the decimal equivalent of given hexadecimal value.
Then, divide decimal value we got from step-2 by 5 keeping notice of the quotient and the remainder.
Continue dividing the quotient by 5 until you get a quotient of zero.
Then just write out the remainders in the reverse order to get quinary equivalent of decimal number.
First, convert 736B.616 into decimal, by using above steps:
= 736B16
= 7 × 1633 × 1626 × 161B × 1606 × 16-1
= 29547.37510
Now, we have to convert 29547.37510 to quinary
29547 / 5 = 5909 with remainder 2
5909 / 5 = 1181 with remainder 4
1181 / 5 = 236 with remainder 1
236 / 5 = 47 with remainder 1
47 / 5 = 9 with remainder 2
9 / 5 = 1 with remainder 4
1 / 5 = 0 with remainder 1
29547 = 1421142 ------- (1)
For converting decimal fraction 0.375 to quinary number, follow these steps:
Multiply 0.375 by 5 keeping notice of the resulting integer and fractional part. Continue multiplying by 5 until you get a resulting fractional part equal to zero (we calcuclate upto ten digits).
Then just write out the integer parts from the results of each multiplication to get equivalent quinary number.
0.375 × 5 = 1 + 0.875
0.875 × 5 = 4 + 0.375
0.375 × 5 = 1 + 0.875
0.875 × 5 = 4 + 0.375
0.375 × 5 = 1 + 0.875
0.875 × 5 = 4 + 0.375
0.375 × 5 = 1 + 0.875
0.875 × 5 = 4 + 0.375
0.375 × 5 = 1 + 0.875
0.875 × 5 = 4 + 0.375
0.375 = 0.1414141414 ------- (2)
29547.37510 = 1421142.14141414145
Therefore, hexadecimal number 736B.6 converted to quinary is equals: