The representation of decimal number 532.86 in the form of binary - decimal isa)1011111b)1011110c)11011110d)10101110Correct answer is option 'B'. Can you explain this answer?

Question

Answer

From binary chart,
• 5=101
• 3= 011
• 2= 010

•• that is, 101011010 would be the answer
• here they removed the zeroes of 2 and 3 at their will.
• anyways i couldn't find this 'formula' used anywhere else. there's a completely different way to solve this.
• and there are no options matching with the other formula

Answer

The correct answer should be C as they are asking about the binary-decimal number i.e. binary number after the decimal which is 86 and this is solved as:

.5 => 1

.25 => 01

.125=> 001

and we want .86 which can be .5+.25+.0625...

which is .110111...

which must be C option

and we can also convert this to decimal and the answer will be.86

Answer

Solution:
To convert a decimal number to binary, we need to follow the below steps:

Step 1: Convert the integer part of the decimal number to binary.

Step 2: Convert the fractional part of the decimal number to binary.

Step 3: Combine the binary representation of the integer and fractional parts.

Step 1: Convert the integer part of the decimal number to binary.

532/2 = 266 remainder 0
266/2 = 133 remainder 0
133/2 = 66 remainder 1
66/2 = 33 remainder 0
33/2 = 16 remainder 1
16/2 = 8 remainder 0
8/2 = 4 remainder 0
4/2 = 2 remainder 0
2/2 = 1 remainder 0
1/2 = 0 remainder 1

The binary representation of the integer part of 532 is 1000010100.

Step 2: Convert the fractional part of the decimal number to binary.

0.86 x 2 = 1.72 -> 1
0.72 x 2 = 1.44 -> 1
0.44 x 2 = 0.88 -> 0
0.88 x 2 = 1.76 -> 1
0.76 x 2 = 1.52 -> 1
0.52 x 2 = 1.04 -> 1
0.04 x 2 = 0.08 -> 0
0.08 x 2 = 0.16 -> 0

The binary representation of the fractional part of 0.86 is 110110.

Step 3: Combine the binary representation of the integer and fractional parts.

The binary representation of the decimal number 532.86 is 1000010100.110110.

On comparing it with the given options, we can see that the correct option is B) 1011110, which is the binary representation of the decimal number 94.

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