Question

Convert the following numbers from the given
to the bases indicated :
decimal 225.225 to binary, octal and hexadecimal
​

Answer 1

Answer:

l high school and work on the way to the gym and then I will be there for a bit more of my life is a factor of my life is a

Answer 2

Binary conversion of $\bf (225.225)_{10}$ is $\bf (11100001.0011100110011001101)_2$

Octal equivalent is $\bf {341.1631464}_8$ and Hexadecimal equivalent is $\bf{E1.399A}_{16}$.

Given:

• A decimal number.
• 225.225

To find:

• Binary conversion
• Octal conversion
• Hexadecimal conversion

Solution:

Step 1: Decimal to Binary conversion.

Case 1: Before decimal point

Divide the number by 2, take whole number as quotient and take number from reverse order.

2|225|1

2|112|0

2|56|0

2|28|0

2|14|0

2|7|1

2|3|1

|1|

Binary conversion of 225 is (11100001)

Case 2: After decimal point.

Multiply the number by 2, take integer number as quotient and multiply again.

0.225×2=0.45 | take 0

0.45×2=0.9 | take 0

0.9×2=1.8 | take 1

0.8×2=1.6 | take 1

0.6×2=1.2| take 1

0.2×2=0.4| take 0

0.4×2=0.8| take 0

0.8×2=1.6| take 1

0.6×2=1.2| take 1

0.2×2=0.4| take 0

0.4×2=0.8 |take 0

0.8×2=1.6 |take 1

0.6×2=1.2 |take 1

and so on...

0.225 in decimal is equivalent to (.0011100110011001101) in binary.

Thus,

Binary conversion of $(225.225)_{10}$ is $\bf (11100001.0011100110011001101)_2$

Step 2:

Convert binary to octal.

Making pair of 3-3 binary digits from right to left before decimal point and left to right after decimal point.

Thus,

011 100 001.001 110 011 001 100 110 100

Write equivalent octal numbers.

000-0

001-1

010-2

011-3

100-4

101-5

110-6

111-7

Thus,

$\bf (225.225)_{10}={341.1631464}_8$

Step 3:

Convert binary to hexadecimal.

Making pair of 4-4 binary digits from right to left before decimal point and left to right after decimal point.

Thus,

1110 0001.0011 1001 1001 1001 1010

Write equivalent hexadecimal numbers for every pair.

Thus,

$\bf (225.225)_{10}={E1.399A}_{16}$

Learn more:

1). The equation (5BC)16 =(x)2 =(y)s, value of x and y

are

(a) x=011010111100, y = 3274

(b) x = 011101101011, y = 3268

(C...

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2) Convert 1010010110011 to HEXADECIMAL and OCTAL

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