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}
Solution:
32_{5} = 3 × 5^{1} + 2 × 5^{0}
32_{5 }= 3 × 5 + 2 × 1
32_{5 }= 15 + 2
32_{5 }= 17
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
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}
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Quinary number system consists of five digits 0 to 4 and its base is ______.
The quinary number system is also known as _______.
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ASK ANY QUESTION ON Quinary Number System
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