Subject: Compulsory Maths
Quinary number system consists of five digits 0 to 4 and its base is 5. It is also known as the base five system. The number of quinary number system can be expressed in the power of 5.
The number is expressed in the power of 5 in order to convert a quinary into decimal number. Then, by simplifying the expanded form of the quinary number, we get a decimal number. For example:
16 = 1× 5^{1} + 6× 5^{0}
= 1× 5 + 6× 1
= 5 + 6
= 11
We can convert a decimal number into quinary number by using the place value table of the quinary system. For example:
Convert 15 into quinary system
5^{4} | 5^{3} | 5^{2} | 5^{1} | 5^{0} |
625 | 125 | 25 | 5 | 1 |
1× 5^{3} | 1× 5^{2} | 0 × 5^{1} | 3× 5^{0} | |
1 | 1 | 0 | 3 |
Here,
153 = 1× 125 + 1× 25 + 0× 5 + 3× 1
= 1× 5^{3} + 1× 5^{2} + 0× 5^{1} + 3× 5^{0}
∴ = 1103_{5}
Alternative method
We should dividethe given number successively by 5 until the quotient is zero in order to convert decimal number int quinary number. The remainders of each successive division are then arranged in reverse order to get required quinary number. For example:
Divisor | Dividend | Remainders |
5 | 134 | 4 |
5 | 26 | 1 |
5 | 5 | 0 |
5 | 1 | 1 |
5 | 0 | |
Now, arranging the remainders in reverse order: 1014_{5}
\(\therefore\) 135 = 1014_{5}
Convert the quinary numbers into decimal numbers.
32_{5}
Solution:
32_{5} = 3 × 5^{1} + 2 × 5^{0}
32_{5 }= 3 × 5 + 2 × 1
32_{5 }= 15 + 2
32_{5 }= 17
Convert quinary numbers into decimal numbers.
1324_{5}
Solution:
1324_{5 }= 1 × 5^{3} + 3 × 5^{2} + 2 × 5^{1} + 4 × 5^{0}
1324_{5 }= 1 × 125 + 3 × 25 + 2 × 5 + 4 × 1
1324_{5 }= 125 + 75 + 10 + 4
1324_{5 }= 214
Convert decimal numbers into quinary numbers.
134
Solution:
5^{4} | 5^{3} | 5^{2} | 5^{1} | 5^{0} |
625 | 125 | 25 | 5 | 1 |
1 × 5^{3} | 0 × 5^{2} | 0 × 5^{1} | 0 × 5^{0} | |
1 | 0 | 1 | 4 |
Here,
134 = 1 × 125 + 0 × 25 + 1 × 5 + 4 × 1
134 = 1 × 5^{3} + 0 × 5^{2 }+ 1 × 5^{1} + 4 × 5^{0}
134 = 1014
∴ 134 = 1014_{5}
Convert 12_{5} into quinary number system into decimal numbers.
Solution:
Here, 12_{5} = 1 × 5^{1} + 2 × 5^{0}
= 1 × 5 + 2 × 1
= 5 + 2
= 7 ans.
Convert 42_{5} into quinary numbers into decimal numbers.
Solution:
Here, 42_{5} = 4 × 5^{1} + 2 × 5^{0}
= 4 × 5 + 2 × 1
= 20 + 2
= 22 ans.
Convert 120_{5} into decimal number system.
Solution:
Here, 120_{5 }= 1 × 5^{2} + 2 × 5^{1} + 0 × 5^{0}
= 1 × 25 + 2 × 5 + 0
= 25 + 10
= 35 ans.
Convert 3042_{5} into decimal number system.
Solution:
Here, 3042_{5} = 3 × 5^{3} + 0 × 5^{2} + 4 × 5^{1} + 2 × 5^{0}
= 3 × 125 + 0 + 4 × 5 + 2 × 1
= 375 + 0 + 20 + 2
= 397 ans.
What is quinary number system? Mention its examples too.
The system which has the base of five in which we use only five digits from 0, 1, 2, 3 and 4 is called the quinary number system. The examples of quinary number system are 102_{5}, 2340_{5}, 34_{5} etc.
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