data representation 2

Introducing:
Hexadecimals Number
System

Hexadecimal number system

From its name alone we can deduct that hexadecimal work as a base-16 numbering system.
Starting from 0 to 9 and then continued with the alphabetical notation of A until F. see the
chart for more details.

Computer itself could not read Hexadecimal, instead they would translate it to binary first.
The reason why hexadecimal exists its to allow us to read it much more easily compared to
binary. Hexadecimal also tends to be shortened into Hex.

Denary

0

1

2

3

4

5

6

7

8

9

11

12

13

14

15

Hex

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F

10

Hexadecimal number system

Few of the common uses for Hex numbers are for HTML code notation for colouring, Error
codes, and Media Access Control (MAC) address

Denary to Hex

163 = 4096

162 = 256

161 = 16

160 = 1

16 * 3 = 48

1 * 7 = 7

48+7=55

Hex= 37

To convert the denary number 55 into hexadecimal we need to calculate how many of
the unit 16 and how many of the unit 1 are required. As hexadecimal is a base-16
system it increases in unit by the power of 16. We can use up to fifteen 1s before we use a 16. We can then use up to a further fifteen 1s before we use the next 16.

The denary number 55 in hexadecimal notation is 37. This means we use three 16s
and seven 1s to create the denary number 55.

Denary to Hex

163 = 4096

162 = 256

161 = 16

160 = 1

16 * 3 = 48

1 * 7 = 7

48+7=55

Hex= 37

To convert the denary number 55 into hexadecimal we need to calculate how many of
the unit 16 and how many of the unit 1 are required. As hexadecimal is a base-16
system it increases in unit by the power of 16. We can use up to fifteen 1s before we use a 16. We can then use up to a further fifteen 1s before we use the next 16.

The denary number 55 in hexadecimal notation is 37. This means we use three 16s
and seven 1s to create the denary number 55.

Denary to Hex

163 = 4096

162 = 256

161 = 16

160 = 1

16 * B (11) = 176

1 * 6 = 6

768+176+6=950

Hex= 3B6

How about number 950?

256* 3 = 768

Open Ended

Convert these numbers to Hex:

20

65

200

1200

Answer

20=14

65=41

200=C8

1200=4B0

Hex to Denary (1)

Hex to denary is much more straightforward. Lets take the number 15 for an example, all we
need to do is to plug in the number into the table, multiply it with the corresponding power
value, and then sum up the results

163 = 4096

162 = 256

161 = 16

160 = 1

16 * 1 = 16

1 * 5 = 5

16

16 + 5 = 21

Hex to Denary (1)

How about the number E9?

163 = 4096

162 = 256

161 = 16

160 = 1

16 * E = 224

1 * 9 = 9

224

224 + 9 = 233

Open Ended

Convert these Hex numbers to Denary

3F

B5

1AB

2F2

Answer

3F=63

B5=181

1AB=427

2F2=754

Bonus!!!

Open Ended

Convert 27F to Denary and 1080 to Hex

Answer

27F=639
1080=438

Hexadecimal and Binary
conversion!

Hexadecimal and Binary conversion!

Converting from Hex number to Binary and vice versa might sound like a daunting task, but using denary we can easily achieve this.

The key lies within this simple equation.

24 = 161

For each 4 digits of binary number we can easily converts it to the corresponding hexadecimal number.

Binary to Hexadecimal and Vice Versa

Lets take the Binary number of 101111001001 for example, first, split the number 4 digits
at a time starting from the far right digit.

The same way could also be said when converting hex to binary. Hex number 938A to Binary!

1011 = 11

1100 = 12

1001 = 9

11 = B

12 = C

9

9

3

8

A = 10

9 = 1001

3 = 0011

8 = 1000

10 = 1010

Bonus!!!

Open Ended

Convert 000111110011 to Hex and DA7 to Binary

Answer

000111110011 =1F3
DA7=110110100111