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Educational Level Secondary school, High school and College
Program Purpose Provide step by step solutions of your problems using online calculators (online solvers)
Problem Source Your textbook, etc

1. Addition, Subtraction, Multiplication, Division of two numbers
1.1 Addition, Subtraction, Multiplication, Division of two numbers in Decimal
1.2 Addition, Subtraction, Multiplication, Division of two numbers in Binary
1.3 Addition, Subtraction, Multiplication, Division of two numbers in Octal
1.4 Addition, Subtraction, Multiplication, Division of two numbers in HexaDecimal
1.5 Addition, Subtraction, Multiplication, Division of two numbers in Other (Eg: Base=6)

2. Conversion From One Base Number To Other Base Number
3. 1's, 2's, 7's, 8's, 9's, 10's, 15's, 16's complement subtraction method
4. Matrix Algebra

5. Computer Orientented Numerical Methods (CONM)
6. Computer Orientented Statistical Methods (COSM)
7. Operation Research (OR)
In Decimal
1. Find addition of 2760 and 796
1 1
2 7 6 0
+ 0 7 9 6

3 5 5 6
2. Find Subtraction of 2760 and 796

16 15
1 6 5 10
2 7 6 0
- 0 7 9 6

1 9 6 4
3. Find multiplication of 2760 and 796
2760
× 796

1932000
248400
16560

2196960
4. Find division of 276 and 6

  
46
  
  
  
6|
276
  
 |
24 
  
 |
  
 |
36
  
 |
36
  
 |
  
 |
0
  

 
Here, Divisor = 6
Dividend = 276
Quotient = 46
Remainder = 0
In Binary
1. Find addition of (1001)2 and (101)2

1
1 0 0 1
+ 0 1 0 1

1 1 1 0
Find Subtraction of (1001)2 and (101)2

0 2
1 0 0 1
- 0 1 0 1

0 1 0 0
3. Find multiplication of (1001)2 and (101)2

1001
× 101

100100
00000
1001

101101
4. Find division of (1001)2 and (101)2

  
1
  
  
  
101|
1001
  
 |
101
  
 |
  
 |
100
  

 
Here, Divisor = 101
Dividend = 1001
Quotient = 1
Remainder = 100
 
In Octal
1. Find addition of (321)8 and (47)8

1
3 2 1
+ 0 4 7

3 7 0
2. Find Subtraction of (321)8 and (47)8

9
2 1 9
3 2 1
- 0 4 7

2 5 2
3. Find multiplication of (321)8 and (47)8

321
× 47

15040
2667

17727
4. Find division of (321)8 and (7)8

  
35
  
  
  
7|
321
  
 |
25 
  
 |
  
 |
51
  
 |
43
  
 |
  
 |
6
  

 
Here, Divisor = 7
Dividend = 321
Quotient = 35
Remainder = 6
In HexaDecimal
1. Find addition of (F34B9)16 and (63C)16

1
F 3 4 B 9
+ 0 0 6 3 C

F 3 A F 5
2. Find Subtraction of (F34B9)16 and (63C)16

2 20 10 25
F 3 4 B 9
- 0 0 6 3 C

F 2 E 7 D
3. Find multiplication of (F34B9)16 and (63C)16

F34B9
× 63C

5B3C5600
2D9E2B0
B678AC

5ECCB15C
4. Find division of (F34B9)16 and (3C)16

  
40E0
  
  
  
3C|
F34B9
  
 |
F0   
  
 |
  
 |
34  
  
 |
0  
  
 |
  
 |
34B 
  
 |
348 
  
 |
  
 |
39
  
 |
0
  
 |
  
 |
39
  

 
Here, Divisor = 3C
Dividend = F34B9
Quotient = 40E0
Remainder = 39
 
In Other (Eg: Base=6)
1. Find addition of (343)6 and (234)6

1 1 1
3 4 3
+ 2 3 4

1 0 2 1
2. Find Subtraction of (343)6 and (234)6

3 9
3 4 3
- 2 3 4

1 0 5
3. Find multiplication of (343)6 and (234)6

343
× 234

113000
15130
2300

134430
4. Find division of (343)6 and (5)6

  
43
  
  
  
5|
343
  
 |
32 
  
 |
  
 |
23
  
 |
23
  
 |
  
 |
0
  

 
Here, Divisor = 5
Dividend = 343
Quotient = 43
Remainder = 0
 
1. Decimal to Binary
(42)10 = (__________)2
(124)10 = (__________)2
(24.625)10 = (__________)2
(42.5)10 = (__________)2

1. Convert Decimal number (42)10 to Binary number

(42)10 = (_______)2

2|42|  





  
2|21|0 





 
2|10|1 





 
2|5|0 





 
2|2|1 





 
2|1|0 





 
|0|1 

∴ (42)10 = (101010)2
2. Decimal to Octal
(425)10 = (__________)8
(1425)10 = (__________)8
(3445.865)10 = (__________)8
(1423.25)10 = (__________)8

1. Convert Decimal number (425)10 to Octal number

(425)10 = (_______)8

8|425|  





  
8|53|1 





 
8|6|5 





 
|0|6 

∴ (425)10 = (651)8
 
3. Decimal to Hexadecimal
(1423)10 = (__________)16
(42356)10 = (__________)16
(4234.456)10 = (__________)16
(1234.567)10 = (__________)16

1. Convert Decimal number (1423)10 to Hexadecimal number

(1423)10 = (_______)16

16|1423|  





  
16|88|F 





 
16|5|8 





 
|0|5 

∴ (1423)10 = (58F)16
4. Binary to Decimal
(110101001)2 = (__________)10
(1100111101)2 = (__________)10
(11010.1001)2 = (__________)10
(11011.101001)2 = (__________)10

1. Convert Binary number (110101001)2 to Decimal number

(110101001)2 = (_______)10

110101001
= 1 × 20 + 0 × 21 + 0 × 22 + 1 × 23 + 0 × 24 + 1 × 25 + 0 × 26 + 1 × 27 + 1 × 28
= 1 × 1 + 0 × 2 + 0 × 4 + 1 × 8 + 0 × 16 + 1 × 32 + 0 × 64 + 1 × 128 + 1 × 256
= 425
∴ (110101001)2 = (425)10
 
5. Binary to Octal
(11011001)2 = (__________)8
(11110101001)2 = (__________)8
(111101.01001)2 = (__________)8
(11110101.00101001)2 = (__________)8

1. Convert Binary number (11011001)2 to Octal number

(11011001)2 = (_______)8


011 011 001
3 3 1

∴ (11011001)2 = (331)8
6. Binary to Hexadecimal
(11110101001)2 = (__________)16
(111101010110001)2 = (__________)16
(11110.101001)2 = (__________)16
(111101.1101001)2 = (__________)16

1. Convert Binary number (11110101001)2 to Hexadecimal number

(11110101001)2 = (_______)16


0111 1010 1001
7 A 9

∴ (11110101001)2 = (7A9)16
 
7. Octal to Decimal
(1534)8 = (__________)10
(12340)8 = (__________)10
(127.32)8 = (__________)10
(432.12)8 = (__________)10

1. Convert Octal number (1534)8 to Decimal number

(1534)8 = (_______)10

1534
= 4 × 80 + 3 × 81 + 5 × 82 + 1 × 83
= 4 × 1 + 3 × 8 + 5 × 64 + 1 × 512
= 860
∴ (1534)8 = (860)10
8. Octal to Binary
(4321)8 = (__________)2
(12345)8 = (__________)2
(123.45)8 = (__________)2
(7012.053)8 = (__________)2

1. Convert Octal number (4321)8 to Binary number

(4321)8 = (_______)2


4 3 2 1
100 011 010 001

∴ (4321)8 = (100011010001)2
 
9. Octal to Hexadecimal
(7012)8 = (__________)16
(123456)8 = (__________)16
(1234.567)8 = (__________)16
(703.056)8 = (__________)16

1. Convert Octal number (7012)8 to Hexadecimal number

First Method
(7012)8 = (_______)16

First Converting Base-8 to Base-2(7012)8 = (_______)2


7 0 1 2
111 000 001 010

∴ (7012)8 = (111000001010)2

Now Converting Base-2 to Base-16(111000001010)2 = (_______)16


1110 0000 1010
E 0 A

∴ (111000001010)2 = (E0A)16

∴ (7012)8 = (E0A)16

OR

Second Method
(7012)8 = (_______)16

First Converting Base-8 to Base-10(7012)8 = (_______)10

7012
= 2 × 80 + 1 × 81 + 0 × 82 + 7 × 83
= 2 × 1 + 1 × 8 + 0 × 64 + 7 × 512
= 3594
∴ (7012)8 = (3594)10

Now Converting Base-10 to Base-16(3594)10 = (_______)16

16|3594|  





  
16|224|A 





 
16|14|0 





 
|0|E 

∴ (3594)10 = (E0A)16
∴ (7012)8 = (E0A)16
10. Hexadecimal to Octal
(FC3A)16 = (__________)8
(ABCD)16 = (__________)8
(1524.03)16 = (__________)8
(BCF.52A)16 = (__________)8

1. Convert Hexadecimal number (FC3A)16 to Octal number

First Method
(FC3A)16 = (_______)8

First Converting Base-16 to Base-2(FC3A)16 = (_______)2


F C 3 A
1111 1100 0011 1010

∴ (FC3A)16 = (1111110000111010)2

Now Converting Base-2 to Base-8(1111110000111010)2 = (_______)8


001 111 110 000 111 010
1 7 6 0 7 2

∴ (1111110000111010)2 = (176072)8

∴ (FC3A)16 = (176072)8

OR

Second Method
(FC3A)16 = (_______)8

First Converting Base-16 to Base-10(FC3A)16 = (_______)10

FC3A
= A × 160 + 3 × 161 + C × 162 + F × 163
= 10 × 1 + 3 × 16 + 12 × 256 + 15 × 4096
= 64570
∴ (FC3A)16 = (64570)10

Now Converting Base-10 to Base-8(64570)10 = (_______)8

8|64570|  





  
8|8071|2 





 
8|1008|7 





 
8|126|0 





 
8|15|6 





 
8|1|7 





 
|0|1 

∴ (64570)10 = (176072)8
∴ (FC3A)16 = (176072)8
 
11. Hexadecimal to Binary
(A35)16 = (__________)2
(BBA)16 = (__________)2
(1085.FB)16 = (__________)2
(FC.3A)16 = (__________)2

1. Convert Hexadecimal number (A35)16 to Binary number

(A35)16 = (_______)2


A 3 5
1010 0011 0101

∴ (A35)16 = (101000110101)2
12. Hexadecimal to Decimal
(7036)16 = (__________)10
(BCA)16 = (__________)10
(A0.36)16 = (__________)10
(100.35)16 = (__________)10

1. Convert Hexadecimal number (BCA)16 to Decimal number

(BCA)16 = (_______)10

BCA
= A × 160 + C × 161 + B × 162
= 10 × 1 + 12 × 16 + 11 × 256
= 3018
∴ (BCA)16 = (3018)10
 
13. Decimal to Other
(1536)10 = (__________)6
(5336)10 = (__________)14
(45236)10 = (__________)24
(155436)10 = (__________)18

1. Convert Decimal number (383)10 to Base 20 number (_______)20

(383)10 = (_______)20

20|383|  





  
20|19|3 





 
|0|J 

∴ (383)10 = (J3)20
14. Other to Decimal
(155436)7 = (__________)10
(BA012)12 = (__________)10
(GH012)20 = (__________)10
(1230321)4 = (__________)10

1. Convert (64X)35 means 64X where its Base 35 to Decimal number

(64X)35 = (_______)10

64X
= X × 350 + 4 × 351 + 6 × 352
= 33 × 1 + 4 × 35 + 6 × 1225
= 7523
∴ (64X)35 = (7523)10
 
1. 1's complement subtraction method
Find Subtraction of 10010 and 1101 using 1's complement method

10010 - 01101 = ??? using 1's Complement
1's Complement of 01101 = 10010
1 1
1 0 0 1 0
+ 1 0 0 1 0

1 0 0 1 0 0

Add carry...
0 0 1 0 0
+ 0 0 0 0 1

0 0 1 0 1

Final answer = 00101
2. 2's complement subtraction method
Find Subtraction of 10010 and 01101 using 2's complement method

10010 - 01101 = ??? using 2's Complement
2's Complement of 01101 = 10011
1 1
1 0 0 1 0
+ 1 0 0 1 1

1 0 0 1 0 1

Ignore carry...
Final answer = 00101
 
3. 7's complement subtraction method
Find Subtraction of 2120 and 543 using 7's complement method

2120 - 0543 = ??? using 7's Complement
7's Complement of 0543 = 7234
1
2 1 2 0
+ 7 2 3 4

1 1 3 5 4

Add carry...
1 3 5 4
+ 0 0 0 1

1 3 5 5

Final answer = 1355
4. 8's complement subtraction method
Find Subtraction of 2120 and 543 using 8's complement method

2120 - 0543 = ??? using 8's Complement
8's Complement of 0543 = 7235
1
2 1 2 0
+ 7 2 3 5

1 1 3 5 5

Ignore carry...
Final answer = 1355
 
5. 9's complement subtraction method
Find Subtraction of 96538 and 9250 using 9's complement method

96538 - 09250 = ??? using 9's Complement
9's Complement of 09250 = 90749
1 1 1
9 6 5 3 8
+ 9 0 7 4 9

1 8 7 2 8 7

Add carry...
8 7 2 8 7
+ 0 0 0 0 1

8 7 2 8 8

Final answer = 87288
6. 10's complement subtraction method
Find Subtraction of 96538 and 9250 using 10's complement method

96538 - 09250 = ??? using 10's Complement
10's Complement of 09250 = 90750
1 1
9 6 5 3 8
+ 9 0 7 5 0

1 8 7 2 8 8

Ignore carry...
Final answer = 87288
 
7. 15's complement subtraction method
Find Subtraction of E68D and 74E using 15's complement method

E68D - 074E = ??? using 15's Complement
15's Complement of 074E = F8B1
1 1
E 6 8 D
+ F 8 B 1

1 D F 3 E

Add carry...
D F 3 E
+ 0 0 0 1

D F 3 F

Final answer = DF3F
8. 16's complement subtraction method
Find Subtraction of E68D and 74E using 16's complement method

E68D - 074E = ??? using 16's Complement
16's Complement of 074E = F8B2
1 1
E 6 8 D
+ F 8 B 2

1 D F 3 F

Ignore carry...
Final answer = DF3F
 
 
4. Matrix Algebra
1. Addition of two matrix
2. Multiplication of two matrix
3. Power of a matrix
4. Transpose of a matrix
5. Deteminant of a matrix
6. Adjoint of a matrix
7. Inverse of a matrix
8. Prove that any two matrix expression is equal or not
9. Minor of a matrix
10. Cofactor of a matrix
11. Trace of a matrix

12. Reduce matrix
13. Rank of matrix
14. Characteristic polynomial
15. Eigen value
16. Eigen vector
 
5. Computer Oriented Numerical Method (Conm)
1. Find a root an equation using
1. Bisection Method
2. False Position Method
3. Iteration Method
4. Newton Raphson Method
5. Secant Method
6. Birge-Vieta method (for `n^(th)` degree polynomial equation)

2. Solve simultaneous equations using
1. Inverse Matrix method
2. Cramer's Rule method
3. Gauss Elimination (Jordan) method
4. Gauss Elimination (Back Substitution) method
5. Gauss Sield method
6. Gauss Jacobi method

3. Numerical Differentiation using Newton's Forward, Backward method
4. Numerical Integration using Trapezoidal, Simpson 1/3, Simpson 3/8 Rule
5. Numerical Interpolation using Forward, Backward, Divided Difference, Langrange's Interpolation method

6. Numerical Differential Equation Solving using Euler, Runge-kutta (Rk2, Rk3, Rk4) methods
 
6. Computer Orientented Statistical Methods (COSM)
1. Mean, Median, Mode, Quartiles, Delices, Percentiles, Variance, Standard deviation for
1. Ungrouped data
2. Grouped data
3. Mixed Type data

2. Missing frequency
1. Frequency for ungrouped data
2. Frequency for grouped data

3.Statistics Graph
1. Histogram
2. Frequency Polygon
3. Frequency Curve
4. Less than type cumulative frequency curve
5. More than type cumulative frequency curve

4. Statistics Wording Problem

5. Arithmetic Mean, Geometric Mean, Harmonic Mean
1. Find Arithmetic mean(AM), Geometric mean(GM), Harmonic mean(HM)
2. Find X from Arithmetic mean(AM), Geometric mean(GM), Harmonic mean(HM)
3. Find Mean or Median or Mode from other two's

6. Combined Mean and Combined Standard deviation

7. Mean deviation about mean, median, mode for
1. Ungrouped data
2. Grouped data

8. Standard deviation and coefficient of variation for
1. Ungrouped data
2. Grouped data
3. Mixed data

9. Correlation Coefficient for
1. Ungrouped data
2. Grouped data

10. Rank Correlation Coefficient

11. Regression and Regression lines
1. Regression lines for X & Y and Class-X & Y
2. Regression from Regression Lines
3. Regression lines from average, standard deviation, Correlation Coefficient(r)
4. Regression lines from `sum x, sum y, sum x^2, sum y^2, sum xy, n`

12. Regression lines for Grouped data

13. Curve Fitting - Method of Least Square
1. straight line `(y=a+bx)`
2. second degree parabola `(y=a+bx+cx^2)`
3. cubic quation `(y=a+bx+cx^2+dx^3)`
 
7. Operation Research (OR)
1. Assignment problem
1.1 Assignment problem (Using Hungarian Method)
1.2 Travelling salesman problem
1.3 Crew assignment problem

2. Simplex Method (Solve linear programming problem using)
1. Simplex Method
2. BigM Method
3. Two-Phase Method
4. Dual Simplex Method
5. Integer Simplex Method (Gomory's cutting plane method)
6. Graphical Method
7. Primal to dual conversion

3. Transportation Problem using
1. North-West corner method
2. Least cost method
3. Vogel's approximation method
4. Optimal solution using MODI method
5. Optimal solution using stepping stone method

4. PERT and CPM

5. Sequencing Problems

6. Replacement and Maintenance Models
1. Model-1 : Replacement policy for items whose running cost increases with time and value of money remains constant during a period
1.1 Model-1.1
1.2 Model-1.2
1.3 Model-1.3
2. Model-2 : Replacement policy for items whose running cost increases with time but value of money changes constant rate during a period
3. Model-3 : Group replacement policy

7. Game Theory
1. Saddle Point
2. Dominance Method
3. Algebraic Method
4. Calculus Method
5. Arithmetic Method
6. Matrix Method
7. 2Xn Games
8. Graphical Method
9. LPP Method
 

 
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