As
we have already learned in the previous topic, theoretically there can exist
and infinite number of bases as any positive number can be made into a base.
But for today we’ll only be focusing on 3 types of bases which are binary, decimal
and hexadecimal. As the title stated, we are going to learn about the
conversion of a number betweean bases. Lets say you are given a decimal number
with value 10, you can turn it into a binary number or a hexadecimal number. Therefore, we’re here
to share with you on the how to? that you have been wondering about.
Part 1: Converting a decimal number into a
binary and vice versa
Example 1:
Given a decimal number with value 15, convert
the given number into binary digit of 8bits.
Step 1: Do a table which reads from right to
left with number 2 as the base number.
2^7

2^6

2^5

2^4

2^3

2^2

2^1

2^0

128

64

32

16

8

4

2

1

Side Note: The “^” sign is the power sign for
those of you who didn’t know about it. Thus, it is read as
2 to the power of 0 and ect.
Step 2: For each of the column insert ones and
multiply them with the upper row number to get a total of
15.
The rest of the column is filled zeros
2^7

2^6

2^5

2^4

2^3

2^2

2^1

2^0

128

64

32

16

8

4

2

1

0

0

0

0

1

1

1

1

Step 3: Write the answer according to the
number of bits asked in the question.
Therefore,
the answer to example 1 is 00001111.
Example2:
Given a binary number of value 10010010.
Convert the following number to a decimal number.
Step 1: Build a table just like in example 1.
2^7

2^6

2^5

2^4

2^3

2^2

2^1

2^0

128

64

32

16

8

4

2

1

Step 2: For each bit from left to right, fill
it in the table in the same order(left to right).
2^7

2^6

2^5

2^4

2^3

2^2

2^1

2^0

128

64

32

16

8

4

2

1

1

0

0

1

0

0

1

0

Step 3: Multiply the bits with the upper row
and add all of the numbers to get the answer.
Answer
= (1*128)+(0*64)+(0*32)+(1*16)+(0*8)+(0*4)+(0*2)+(0*1)
= 146
Thus, that concludes part 1 of today’s topic.
Next, we’re going to convert numbers involving the hexadecimal system.
Part 2: Converting decimal to hexadecimal
number and vice versa.
Example 1:
Given a decimal number with value 273. Convert
the following number into a hexadecimal number.
Step 1: Build a table.
16^4

16^3

16^2

16^1

16^0

65536

4096

256

16

1

Step2: Insert the numbers in their proper
column.
16^4

16^3

16^2

16^1

16^0

65536

4096

256

16

1

0

0

1

1

1

Step 3: Answer = ???
Answer
= 111
Example 2:
Given 3FEA. Convert the following number into
a decimal number.
Step 1: Define the alphabets.
A
= 10, E = 14, F = 15, 3 = 3
Step 2: Build a table with base 16.
16^3

16^2

16^1

16^0

4096

256

16

1

3

15

14

10

Step 3: Multiply the numbers with the upper
row and add them together to get the value.
Answer
= (3*4096) + (15*256) + (14*16) + (10*1)
= 16362
Part 3: Converting a hexadecimal number to
binary digits and vice versa
Example 1:
Given FEA31. Convert the following hexadecimal
number to binary digits.
Step 1: Convert each characters to their
respective binary digits.
F
= 15, E = 13, A = 10, 3 = 3, 1 = 1
2^4

2^3

2^2

2^1

2^0

Step 2: Write the answer.
F = 15 = 1111, E = 14 = 1110, A = 10 = 1010, 3
= 3 = 0011, 1 = 1 = 0001
Answer = 11111110101000110001
PS: You can refer to the table given for
easier conversion.
Example 2:
Given 1110111100011010. Convert the following
to its hexadecimal number system.
Step 1: Split the digits to 4bit each.
1110 1111 0001
1010
(a) (b) (c) (d)
Step 2: For each (a), (b), (c) and (d) refer
to the table given or convert them into hexa numbers using
the table formula.
16^3

16^2

16^1

16^0

Step 3: Write the answer.
1110 = 14 = E,
1111 = 15 = F,
0001 = 1,
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