Hexadecimal Division Examples

This is my fourth and last article on hexadecimal arithmetic. In this post I will solve some examples on hexadecimal number system division. Before starting this topic you should know how to multiply hexadecimal numbers. Here is my article on hexadecimal numbers multiplication.

Key Questions:

• How to perform division base 16 or hexadecimal number system?
• How to perform division on fractional hexadecimal numbers?

Hexadecimal Division Examples:

The hexadecimal numbers division is same as the division performs in other number systems. All the rules and principles are same. You can verify your results by using this online calculator.

5÷6  in this 5 is dividend and 6 is divisor

I will discuss three cases with the help of three examples. In first case dividend and divisor both are integers. In second case dividend has a fractional part while divisor is an integer. In third cas both dividend and divisor have fractional parts.

Example#01:AE887)16÷3A)16

First make multiplication table for 3A and it's multiples

3A*1	3A
3A*2	74
3A*3	AE
3A*4	E8
3A*5	122
3A*6	15C
3A*7	196
3A*8	1D0
3A*9	20A
3A*A	244
3A*B	27E

                  3025.A3

         3A⟌AE887  

                 AE      

                   X88

                      74

                      147

                      122

                        250

                        244

                           B0

                           AE

                             2

Answer:3025.A3)16

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Example#02:ECE.46)16÷12)16

First make multiplication table for 12

12*1	12
12*2	24
12*3	36
12*4	48
12*5	5A
12*6	6C
12*7	7E
12*8	90
12*9	A2
12*A	B4
12*B	C6
12*C	D8
12*D	EA

 

                       D2.92

         12⟌ECE.46

                 EA

                    2E

                    24

                      A4

                      A2

                         26

                         24

                           2

Answer:D2.92)16

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Example#03:257.8A)16÷5.1)16

Shifting hexadecimal point makes the problem easy. According to mathematical rule if you shift hexadecimal point of the dividend upto one place then you have to shift the hexadecimal point of the divisor.

After shifting

2578.A÷51

51*1	51
51*2	A2
51*3	F3
51*4	144
51*5	195
51*6	1E6
51*7	237
51*8	288
51*9	2D9
51*A	32A
51*B	37B
51*C	3CC
51*D	41D

                         76.6D

         51⟌2578.A

                 237

                   208

                  1E6

                     22A

                     1E6

                       440

                       41D

                          33

                                   

Answer: 76.6D)16

Hexadecimal Multiplication Examples

This is my third article on hexadecimal arithmetic. In this post I will explain how to multiply two hexadecimal numbers. It is same as we multiply numbers in other number systems. Before starting hexadecimal multiplication you should know the hexadecimal addition. Here are my articles on hexadecimal addition and hexadecimal subtraction.

Key Questions:

• How to perform multiplication on hexadecimal number system?
• How to perform fractional hexadecimal numbers multiplication?

Hexadecimal Multiplication Table:

X	0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
1	0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
2	0	2	4	6	8	A	C	E	10	12	14	16	18	1A	1C	1E
3	0	3	6	9	C	F	12	15	18	1B	1F	21	24	27	2A	2D
4	0	4	8	C	10	14	18	1C	20	24	28	2C	30	34	38	3C
5	0	5	A	F	14	19	1E	23	28	2D	32	37	3C	41	46	4B
6	0	6	C	12	18	1E	24	2A	30	36	3C	42	48	4E	54	5A
7	0	7	E	15	1C	23	2A	31	38	3F	46	4D	54	5C	63	6A
8	0	8	10	18	20	28	30	38	40	48	50	58	60	68	70	78
9	0	9	12	1B	24	2D	36	3F	48	51	5A	63	6C	75	7E	87
A	0	A	14	1E	28	32	3C	46	50	5A	64	6C	78	82	8C	96
B	0	B	16	21	2C	37	42	4D	58	63	6E	79	84	8F	9A	A5
C	0	C	18	24	30	3C	48	54	60	6C	78	84	90	9C	A8	B4
D	0	D	1A	27	34	41	4E	5B	68	75	82	8F	9C	A9	B6	C3
E	0	E	1C	2A	38	46	54	62	70	7E	8C	9A	A8	B6	C4	D2
F	0	F	1E	2D	3C	4B	5A	69	78	87	96	A5	B4	C3	D2	E1

How to use hexadecimal multiplication table:

Look at first row (red), it is X

Look at first column (blue), it is Y

Look at the rest of the table, these values are product of X and Y

For example 5*D: X=5,Y=D

Find value at the intersection of column 5 (X=5) and row D(Y=D)

5*D=41

Hexadecimal Multiplication Examples:

Example#01:75)16*DA)16

             4

       3

       7 5

     *D A

  1 4 9 2

 5 F 1 X

 6 3 A 2

X	Y	Hexadecimal	Sum	Carry
5	A	32	2	3
7	A	46+3=49	9	4
5	D	41	1	4
7	D	5B+4=5F	F	5
		4+F=13	3	1

Answer:63A2)16

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Example#02:6AB)16*A9)16

                 6   6

          6   6

         6 A B

      1  *A 9

      3 C 0 3

   4 2 A E X

   4 6 6 E 3

X	Y	Hexadecimal	Sum	Carry
B	9	63	3	6
A	9	5A+6=60	0	6
6	9	36+6=3C	C	3
B	A	6E	E	6
A	A	64+6=6A	A	6
6	A	3C+6=42	2	4
		C+A=16	6	1

Answer:466E3)16

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Example#03:769.E2)16*8.A)16

                             3   4    7     1

                 4  6  8   1

                7 6 9 . E 2

                   1    *8 . A

               4 A 2 2 D 4

            3 B 4 F 1 0 X

             3 F F 1 . 3 D 4

X	Y	Hexadecimal	Sum	Carry
2	A	14	4	1
E	A	8C+1=8D	D	8
9	A	5A+8=62	2	6
6	A	3C+6=42	2	4
7	A	46+4=4A	A	4
2	8	10	0	1
E	8	70+1=71	1	7
9	8	48+7=4F	F	4
6	8	30+4=34	4	3
7	8	38+3=3B	B	3

Answer:3FF1.3D4)16

I checked and verified each example and multiplication table. If you still find any mathematical, typographical or logical mistake please inform me. I will grateful to you. 

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