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12 * 2^10 = 12,288 bytes, and the question is about bits (8 bits in a byte).
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<div>As for the colors, you don’t really have to consider RGB when counting the bits. In the “old days” when monitors could not display 24-bit color, we used look-up tables to get different color palettes. 8-bit color was a common case, and GIF files still
use 8-bit color. There are only 256 different colors, but which ones they are is controlled by a color look-up table. Each 8-bit value (between 0 and 255) is used to look in a table of colors. Each table entry has a regular 24-bit RGB value for that color.
The 6 bits in your question could be used to form a 64-entry look-up table.</div>
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<div>Another way to interpret it, however, is that the 6 bits are split up evenly between R, G, and B, so there are 2 bits for each color channel. There are a total of 2^6 = 64 different colors, and each channel has 2^2 = 4 different variations.</div>
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<div>James<br>
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<div>Dr. James Vanderhyde</div>
<div>Math and Computer Science</div>
<div>Benedictine College</div>
<div><a href="mailto:jvanderhyde@benedictine.edu">jvanderhyde@benedictine.edu</a></div>
<div><a href="http://vanderhyde.us/~james/pro/">http://vanderhyde.us/~james/pro/</a></div>
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<div>On Mar 5, 2014, at 12:30 AM, Sandy Graham <<a href="mailto:sandyg@gvtc.com">sandyg@gvtc.com</a>> wrote:</div>
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<span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);">The book I just started has this question:<o:p></o:p></span></p>
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<span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);">“If a picture was made up of 64 possible colors, how many bits would be needed to store each pixel of the picture?”<o:p></o:p></span></p>
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<span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);">I thought RGB values would be required so was trying to figure out an answer from that (though the book doesn’t give much information on how to do that exactly), but the
answer key says the answer is 6. I can see that 2^6 = 64 and assume that’s where the 6 came from, but why is that the answer? How does 6 bits yield 64 possible colors? Don’t RGB values have to be considered?<o:p></o:p></span></p>
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<span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);">Then the next question asks, “How many bits are there in 12 KB?”<o:p></o:p></span></p>
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<span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);">So 12 * 2^10 = 12,288, right? I’m pretty confident of my answer, but I wanted to double check with a reliable source as the answer key says 98, 304 is the correct answer.
The key is wrong, right?<o:p></o:p></span></p>
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<span style="font-size: 11pt; font-family: Calibri, sans-serif; color: rgb(31, 73, 125);">Thanks! I didn’t know where else I could get a reliable answer to this!<o:p></o:p></span></p>
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<span style="font-size: 14pt; font-family: 'Brush Script MT'; color: rgb(31, 73, 125);">Your sister in Christ,<o:p></o:p></span></div>
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<span style="font-size: 14pt; font-family: 'Brush Script MT'; color: rgb(31, 73, 125);">Sandy Graham<o:p></o:p></span></div>
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