How Do You Convert Hexadecimal 2CC to Binary?

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Discussion Overview

The discussion revolves around the conversion of hexadecimal values to binary, specifically focusing on the hexadecimal number 2CC and its binary equivalent. Participants explore different methods of conversion, addressing both whole numbers and fractional components in hexadecimal notation.

Discussion Character

  • Homework-related, Technical explanation, Conceptual clarification

Main Points Raised

  • Some participants propose that converting hexadecimal to binary involves converting each hex digit to its binary equivalent, suggesting that 2CC in binary is 0010 1100 1100.
  • Others question whether it is necessary to find binary values that sum to the decimal equivalent (716) or to convert hex digits separately.
  • A participant mentions that converting from hex to binary is straightforward and does not require summing powers of 2.
  • There is a discussion about extending the conversion to hexadecimal numbers with fractional parts, such as 2CC.AB851EB, and whether the same conversion rules apply.
  • Some participants confirm that the conversion process remains consistent regardless of the hexadecimal number's complexity, including examples with both whole numbers and fractions.
  • One participant emphasizes the ease of converting between hex and binary compared to converting to and from decimal.
  • Another participant raises a question about converting a different hexadecimal number (42.2B) to binary, seeking clarification on whether the same conversion principles apply.

Areas of Agreement / Disagreement

Participants generally agree on the method of converting hexadecimal to binary by treating each digit separately. However, there is some uncertainty regarding the necessity of summing powers of 2 versus direct conversion. The discussion remains unresolved on the implications of fractional hexadecimal values.

Contextual Notes

Some participants express confusion about the conversion process, particularly regarding the treatment of whole numbers versus fractions in hexadecimal notation. There are also references to the relationship between powers of 2 and powers of 16 in the context of conversion.

Aristotle
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Homework Statement


After being given a decimal base 10 #: 716, I've converted it to hexidecimal and got 2CC. However, if I want to convert 2CC to BINARY, do I find numbers of base 2s that ADD up to 716 ( 1011001110) OR do I find binary values for 2 , C , C separately? (Such as 0010 1100 1100)

Homework Equations


Bases of 2 values:

512 256 128 64 32 16 8 4 2 1
 
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Aristotle said:

Homework Statement


After being given a decimal base 10 #: 716, I've converted it to hexidecimal and got 2CC. However, if I want to convert 2CC to BINARY, do I find numbers of base 2s that ADD up to 716 ( 1011001110) OR do I find binary values for 2 , C , C separately? (Such as 0010 1100 1100)

Homework Equations


Bases of 2 values:

512 256 128 64 32 16 8 4 2 1
Converting from hex to binary is very simple: just convert each hex digit to its binary equivalent. So 2CC16 is just as you have it, 0010 1100 11002. All the powers of 2 are automatically taken care of.
 
Mark44 said:
Converting from hex to binary is very simple: just convert each hex digit to its binary equivalent. So 2CC16 is just as you have it, 0010 1100 11002. All the powers of 2 are automatically taken care of.
Ah okay so in never the case you never want to expand the bases to find what sums to 716...but have to break them apart in 4 bits?
 
Aristotle said:
Ah okay so in never the case you never want to expand the bases to find what sums to 716...but have to break them apart in 4 bits?
I'm not sure I understand your question. If you have converted 71610 to hex, you have already done all of the hard work. Going one more step in converting hex to binary is very simple -- just convert each hex digit to its binary equivalent.
 
Either. But when you realize that, you will see that one of your answers has an error. Find which one, and you should be happy.
 
Mark44 said:
I'm not sure I understand your question. If you have converted 71610 to hex, you have already done all of the hard work. Going one more step in converting hex to binary is very simple -- just convert each hex digit to its binary equivalent.

So let's say my Hexidecimal value was actually 2CC.AB851EB...to Binary it would be 0010 1100 1100. 1010 1011 1000 0101 1110 1011 ?
 
Aristotle said:
So let's say my Hexidecimal value was actually 2CC.AB851EB...to Binary it would be 0010 1100 1100. 1010 1011 1000 0101 1110 1011 ?
Yes. I'm assuming that you have converted each hex digit correctly -- I didn't check.

A simpler example would be 10.2510. In hex, this would be A.4 (10 + 4/16). The direct binary conversion would be 1010.0100 . This is not how numbers with decimal fractions are actually stored, but I don't think that's what you're concerned with.
 
Mark44 said:
Yes. I'm assuming that you have converted each hex digit correctly -- I didn't check.

A simpler example would be 10.2510. In hex, this would be A.4 (10 + 4/16). The direct binary conversion would be 1010.0100 . This is not how numbers with decimal fractions are actually stored, but I don't think that's what you're concerned with.
Thank you for the help!
 
Mark44 said:
Yes. I'm assuming that you have converted each hex digit correctly -- I didn't check.

A simpler example would be 10.2510. In hex, this would be A.4 (10 + 4/16). The direct binary conversion would be 1010.0100 . This is not how numbers with decimal fractions are actually stored, but I don't think that's what you're concerned with.
Wait last question...
So if say I had a NUMBER in hexidecimal like
42.2B ...converting that to BINARY...
just like the example you shown...
would you convert 42 to 0100 0010 ?
 
  • #10
Aristotle said:
Wait last question...
So if say I had a NUMBER in hexidecimal like
42.2B ...converting that to BINARY...
just like the example you shown...
would you convert 42 to 0100 0010 ?
0100 = 4
0010 = 2

Just like with 2CC we did binaries separately. or is numbers an exception?
 
  • #11
Aristotle said:
Wait last question...
So if say I had a NUMBER in hexidecimal like
42.2B ...converting that to BINARY...
just like the example you shown...
would you convert 42 to 0100 0010 ?
Yes.

4216 means 4 X 16 + 2 X 1, right?
In the 0100 group, the rightmost 0 bit is the number of 16s. The next digit to the left (0) is the number of 32's. Continuing to the left, the 1 digit is the number of 64's, but 1 times 64 is the same as 4 times 16. So 0100 0010 means 1 X 64 + 2 X 1, which is the same as 4 X 16 + 2 X 1. Instead of dealing with all those powers of 2 (1, 2, 4, 8, etc.), it's easier to deal with powers of 16 (1, 16, 256, 4096, etc.) by clumping each group of four binary digits into one hex digit. As I said, it's very easy going back and forth between hex and binary, but much harder to convert from either of those bases to base 10 or vice versa.
 
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