SOLUTION: Convert the following: a. 9F2Ch to binary Can you please explainb to me the question step-by-step? Thank you!

Question 1191541: Convert the following:
a. 9F2Ch to binary

Can you please explainb to me the question step-by-step? Thank you!
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

I'm assuming you want to convert from the hexadecimal value of 9F2C to binary.

Recall that the base 16 hexadecimal system has these digits
0,1,2,3,4,5,6,7,8,9
A,B,C,D,E,F

Where,
A base 16 = 10 base 10
B base 16 = 11 base 10
C base 16 = 12 base 10
D base 16 = 13 base 10
E base 16 = 14 base 10
F base 16 = 15 base 10

As mentioned,
C base 16 = 12 base 10
Then rewrite 12 as a sum of powers of 2.
12 = 8+4
12 = 2^3 + 2^2
12 = 1*2^3 + 1*2^2 + 0*2^1 + 0*2^0
The string of coefficients 1, 1, 0, 0 in that order leads to the binary representation of 12 base 10 = 1100 base 2.

By extension,
C base 16 = 12 base 10 = 1100 base 2

Through similar logic,
2 base 16 = 0010 base 2

Combining those allows us to say:
2C base 16 = 0010 1100 base 2
Take note of the color coding to see how the split happens.

Also,
9F base 16 = 1001 1111 base 2

Therefore,
9F2C base 16 = 1001 1111 0010 1100 base 2
I recommend you keep the spacing of 4 digits per group to make the binary number more readable.

A handy calculator to check your work
https://www.binaryhexconverter.com/hex-to-binary-converter
Click on the "padding" to have the digits space themselves out into groups of 4.
You can also click on "swap" to convert the other way around (as another way to verify the answer).

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