Note on Quinary Number System

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The quinary number system is a number system having five as the base. There are only five numerals in the quinary number system. They are 0, 1, 2, 3 and 4 in this system. This will represent any real numbers.

Quinary means base 5 so each place is a power of 5.

In this method five is written as 10, twenty-five is written as 100 and sixty is written as 220.

Consider the quinary number of 1555

1555 = 1 x 52 + 5 x51 + 5 x50

= 25 + 25 + 5

= 55

While converting a decimal number into a quinary number, we must divide it by 5 repeatedly and write the remainders until the result of the division is 0. The quinary number is obtained by reading the sequence of the remainders in the reverse order. For example, let's consider the number 8410

84 ÷ 5 = 16 Remainder 4

16 ÷ 5 = 3 Remainder 1

3÷ 5 = 0 Remainder 2

Addition of quinary numbers

Finding arithmetic in a base other than 10 is to understand the notation we use in base 10.

We write the number thirteen as 13, meaning 1 tens and 3 ones. It may help you to think about objects, like sticks. The idea is to make thirteen sticks and arrange them in the group of ten. You get 1 groups of ten and three extra.

Suppose, if you add 23 and 19 you put together the 3 ones with the 9 ones giving 12 ones, which is 1 ten and 2 extra. That is you get one more group of ten sticks. That is the "carry over". So, altogether you have 2 + 1 + 1 tens and 2 ones, for a sum of 42.

In base-5, you want to collect the objects in groups of five rather than tens. So if you have nine objects you can arrange them into one group of five and 4 ones.

Now to add 2 and 3 using base 5 notation, 2 + 3 = 10 in base 5.

Subtraction of quinary numbers

Subtraction in quinary number is straight forward as we are always subtracting a smaller digit from a large digit. Let's look at a base 10 problem first.

3 2 5

\(\underline{-1 3 4}\)

1 9 1

Starting in the right most column 5 - 4 = 1 but in the next column you need to borrow from the next column. Since this is base 10 notation you are borrowing ten so the 3 in the third column be 2 and adding to 10 to 2 you have 12 in the second column.

Now,

Let's try a base 5 problem

431

\(\underline{-240}\)

141

As in the base 10 problem, the first column is easy, 1 - 0 = 1. In the second you need to borrow from the third column. Since the numbers are written in base 5 notation you are borrowing five so the 4 in the third column becomes 3 and adding five to gives you eight in the second column.

Example:

Convert the following decimal number into a quinary number.

a) 425

Solution:

5 425 0
5 85 0
5 17 2
5 3 3
  0  

∴ 42510 = 32005

  • There are only five numerals 0, 1, 2, 3,  and 4 in quinary number system.
  • Quinary means base 5 so each place is a power of 5.
  • Many languages use the quinary number system.
.

Very Short Questions

Solution:

5 425 0
5 85 0
5

17

2
5 3 3

0

∴ 42510 = 32005

Solution:

5 924 4
5 184 4
5 36 1
5 7 2
5 1 1
0

∴ 92410 = 121445

Solution:

5 924 4
5 184 4
5 36 1
5 7 2
5 1 1
0

∴ 92410 = 121445

Solution:

5 1574 4
5 312 2
5 62 2
5 12 2
5 2 2
0

∴ 157410 = 222245

Solution:

5 2487 2
5 497 2
5 99 4
5 19 4
5 3 3
0

∴ 248710 = 344225

Solution:

5 3040 0
5 608 3
5 121 1
5 24 4
5 4 4
0

∴ 304010 = 441305

Solution:

5 5864 4
5 1172 2
5 234 4
5 46 1
5 9 5
5 1 1
0

∴ 586410 = 1514245

Solution:

5 1574 4
5 312 2
5 62 2
5 12 2
5 2 2
0

∴ 157410 = 222245

Solution:

5 5864 4
5 1172 2
5 234 4
5 46 1
5 9 4
5 1 1
0

∴ 586410 = 1414245

Solution:

2125

= 2× 52 + 1× 51 + 2× 50

= 2× 25 + 1× 5 + 2× 1

= 50 + 5 + 2

= 5710

Solution:

23045

= 2× 53 + 3× 52 + 0× 41 + 4× 50

= 2× 125 + 3× 25 + 0×4 + 4×1

= 250 + 75 +0 +4

= 32910

Solution:

31045

= 3× 53 + 1× 52 + 0×51 + 4× 50

= 3× 125 + 1× 25 + 0×5 + 4×1

= 375 + 25 + 0+ 4

= 40410

Solution:

11102

= 1× 23 + 1× 22 + 1× 21+ 0×20

= 8 + 4 + 2 +0

= 1410

Now,

5 14 4
5 2 2
0

∴ 11102 = 1410 = 245

Solution:

10112

= 1 × 23 + 0× 22 + 1× 21 + 1× 50

= 8 + 0 + 2 + 1

= 1110

Then,

5 11 1
5 2 2
0

∴ 10112 = 1110 = 215

Solution:

11112

= 1× 23 + 1× 22 + 1× 21 + 1×20

= 8 + 4 + 2 + 1

= 1510

Then,

5 15 0
5 3 3
0

∴ 11112 = 1510 = 305

Solution:

21345

= 2× 53 + 1× 52 + 3× 51 + 4× 50

= 250 + 25 + 15 + 4

= 294

Then,

2 244 0
2 122 0
2 61 1
2 30 0
2 15 1
2 7 1
2 3 1
2 1 1
0

∴ 29410 = 111101002

0%
  • Convert the following quinary number into decimal number.

    31045

    40410
    41010
    40510
    41510
  • Convert the following quinary number into decimal number.

    10445

    15510
    17510
    14410
    14910
  • Convert the following quinary number into decimal number.

    2125

    5710
    5810
    5510
    6510
  • Convert the following quinary number into decimal number.

    3145

    9910
    9510
    8510
    8410
  • Convert the following quinary number into decimal number.

    4125

    10510
    10710
    11510
    10810
  • Convert the following decimal number into quinary number.

    672

    102025
    102095
    102505
    102125
  • Convert the following decimal number into quinary number.

    512

    40275
    40255
    40225
    40555
  • Convert the following quinary number into binary number.

    1215

    1010102
    1111112
    1001002
    1101102
  • Convert the following quinary number into binary number.

    4415

    11110012
    10101012
    11001012
    11111112
  • Convert the following quinary number into binary number.

    21345

    111101002
    110011002
    110000012
    111100102
  • Convert the following binary number into quinary number.

    1101102

    2075
    2555
    2045
    2055
  • Convert th efollowin decimal number into quinary number.

    348

    23435
    23405
    23455
    23505
  • Convert the following binary number into quinary number.

    11012

    295
    255
    235
    275
  • Convert the following binary number into quinary number.

    11112

    305
    355
    555
    455
  • Convert the following quinary number into decimal number.

    41325

    54710
    55510
    54210
    54010
  • You scored /15


    Take test again

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