Question 7 - Sample Paper 2 by Teachoo - Teachoo Sample Paper

In the hexadecimal number system, each digit can represent 16 possible values, from 0 to 9 and from A to F. What is the hexadecimal equivalent of the decimal number 127? 

a)7F 

b)8F 

c)7E 

d)8E

Answer:

Answer by student

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a)7F

Detailed answer by teachoo

• To convert a decimal number to a hexadecimal number, we need to divide the decimal number by 16 repeatedly and write the remainder in reverse order.

• For example, to convert 127 to hexadecimal, we can follow these steps:

• The remainder 15 corresponds to the hexadecimal digit F, and the remainder 7 corresponds to the hexadecimal digit 7 . So, we write them in reverse order as 7F .
• Therefore, the hexadecimal equivalent of 127 is 7F .
• We can check our answer by converting 7F back to decimal. We can do this by multiplying each hexadecimal digit by its place value (16^0 for the rightmost digit and 16^1 for the leftmost digit) and adding them up.
• For example, to convert 7F to decimal, we can follow these steps:

• The decimal equivalent of F is 15, and the decimal equivalent of 7 is 7. So, we multiply them by their place values and add them up as (15 x 16^0) + (7 x 16^1) = 15 + 112 = 127.
• Therefore, the decimal equivalent of 7F is 127.

Now, let’s look at the other options and see why they are incorrect.

• Option B: 8F is not the hexadecimal equivalent of 127 , because if we convert it back to decimal, we get (15 x 16^0) + (8 x 16^1) = 15 + 128 = 143, which is not equal to 127.
• Option C: 7E is not the hexadecimal equivalent of 127 , because if we convert it back to decimal, we get (14 x 16^0) + (7 x 16^1) = 14 + 112 = 126, which is not equal to 127.
• Option D: 8E is not the hexadecimal equivalent of 127 , because if we convert it back to decimal, we get (14 x 16^0) + (8 x 16^1) = 14 + 128 = 142, which is not equal to 127.

So, the correct answer is A.

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