Question

convert 736 into quinary system ​

Answer 1

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: