Quinary base five

Number Systems

1. Scanned by CamScanner

2. BY ASSOCIATE PROFESSOR NADEEM UDDIN

Conversion from Decimal number to Quinary number


Example -15 Decimal to Quinary







(412)10 = (3122)5



Conversion from Quinary number to Decimal number


Example -16 Quinary to Decimal


3122 = 3 x 5
3
+ 1 x 5
2
+ 2 x 5
1
+ 2 x 5
0

3122 = 3 x 125 + 1 x 25 + 2 x 5 + 2 x 1

3122 = 375 + 25 + 10 + 2

3122 = 412

(3122)5 = (412)10








5 412
5 82 2
5 16 2
3 1

3. Addition Facts in quinary:

5 = 10
6 = 11
7 = 12
8 = 13 and so on

(a) 2
+ 1
3 (No need to change base)

(b) 3
+ 2
10 (3 + 2 = 5) (5 in base 5 is 10)


(c) 4
+ 3
12 (4 + 3 = 7) (7 in base 5 is 12)

(d) 4
+ 4
13 (4+4 =8) (8 in base 5 is 13)



Example –17

4 3 2 + 3 4 1

Solution: 4 3 2 (2+1 = 3) (No need to change base)
+ 3 4 1 (3+4 = 7) (7 in base 5 is 12)
1 3 2 3 (1+4+3 = 8) (8 in base 5 is 13)



Example- 18

1 2 4 2 1 4 + 4 0 3 3 1 2

Solution:

1 2 4 2 1 4
+ 4 0 3 3 1 2
1 0 3 3 0 3 1

4. Subtraction Facts in quinary:


Example-19

3 2 4 – 1 1 2

Solution:
3 2 4
- 1 1 2
2 1 2


Example-20

4 2 0 4 – 1 2 2 0

Solution:
4 2 0 4 (in substraction, we directly take 5 as carry
-1 2 2 0 and add it in the existing digit).
2 4 3 4 Step 1) 4 – 0 = 4
Step 2) 5 + 0 = 5 now, 5 – 2 = 3
Step 3) We carry 5 and 5 + 1 = 6
now 6 – 2 = 4
Step 4) Now, 3 left 3 – 1 = 2



Multiplication Facts in quinary:



Example-21:

324 x 34
Solution:

3 2 4 (4 x 4 = 16 in penta 16 is 31)
x 3 4 (4 x 2 = 8 + carry = 8 + 3 = 11 in penta 11 is 21)
2 4 1 1 (4 x 3 = 12 + carry = 12 + 2 = 14 in penta 14 is 24)
2 0 3 2 x (3 x 4 = 12 in penta 12 is 22)
________________________________
2 3 2 3 1 (3 x 2 = 6 + carry = 6 + 2 = 8 in penta 8 is 13)
(3 x 3 = 9 + carry = 9 + 1 = 10 in penta 10 is 20)

5. Example-22:

2 4 4 0 3 x 4 2 3 2

Solution:
2 4 4 0 3
x 4 2 3 2
1 0 4 3 1 1
1 3 4 2 1 4 x
1 0 4 3 1 1 x x
2 1 4 1 2 2 x x x
2 3 2 1 1 0 1 0 1


Division Facts in quinary:

Example-23:

1 3 4 ÷ 4

Solution:

First to make table

4 x 1 = 4

4 x 2 = 1 3 (covert 8 into base 5)

21
4 134
-13
x x 4
- 4
x

1 3 4 = 2 1
4

6. Example-24:

4 1 1 4 2 ÷ 1 3

Solution:

First to make table

1 3 x 1 = 1 3

1 3 x 2 = 3 1

1 3 x 3 = 4 4

1 3 x 4 = 1 1 2
2314
13 41142
- 31
1 0 1
4 4
x 2 4
1 3
1 1 2
1 1 2
x x x

4 1 1 4 2 = 2314
1 3

7. Example-25:
2 4 4 2 0÷ 1 1

Solution:

First to make table

1 1 x 1 = 1 1

1 1 x 2 = 2 2

1 1 x 3 = 3 3

1 1 x 4 = 4 4

2220
11 24420

- 2 2
x 2 4
2 2
x 2 2
2 2
x x x

2 4 4 2 0 = 2 2 2 0
11