Answers.Body: <p>Bits are not frequencies. If a position only contains an A (position 3 for example) then you would need 2 questions (bits) to derive that information without a priori knowledge.</p>
  
  <ol>
  <li>Is it a G or C? if no > then it is a A or T</li>
  <li>Is it T? If no then it is an A</li>
  </ol>
  
  <p>Position 1 can be derived by 1 question only:</p>
  
  <ol>
  <li>is it a G or C?  If no then it is an A or T</li>
  </ol>
  
  <p>In this case the number of bits can be calculated using the frequenci)es. </p>
  
  <p><strong>For 4 bases, A only (100%)</strong>:</p>
  
  <p>4 * -0.25 * log2(0.25) - (-1 * log2(1)) = 2 (bits)</p>
  
  <p><strong>For 8 letters, A only (100%)</strong>:</p>
  
  <p>8 * -1/8 * log(1/8)- (-1 * log2(1)) = 3 (bits)</p>
  
  <p><strong>Mixed base possibility (A/T 50% each) with 4 bases</strong>:</p>
  
  <p>4 * -0.25 * log2(0.25) - (-0.5 * log2(0.5)+-0.5 * log2(0.5)) = 1 (bit)</p>
  
  <p>As mentioned in the comments, you can follow the wiki link for an example.</p>
  
  <p>Or, an example with a little more explanation from the biology SE site.</p>
  
  <p><a href="https://biology.stackexchange.com/questions/64368/how-to-determine-the-height-bits-in-a-sequence-logo">sequence logo calcuation</a></p>
  
  <p>Hopes this helps</p>
  
Answers.ContentLicense: CC BY-SA 4.0
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Answers.Text: Thanks for your answer. In this specific case, `4 bases` is being used, since there are a,t,g,c 4 Nucleotides in total, right?
Answers.UserDisplayName: czlsws
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Answers.Text: correct. That is this part: 4 * -0.25 * log2(0.25) of the equation.
Answers.UserDisplayName: Mack123456
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Answers.UserDisplayName: Mack123456
Body: <p>Following <a href="https://bioinformatics.stackexchange.com/questions/9087/what-is-aligned-sequences-and-consensus-sequence-in-the-context-of-sequence">this question</a>, I'm confused with the <a href="https://en.wikipedia.org/wiki/Sequence_logo" rel="nofollow noreferrer">computation of sequence logo</a> </p>
  
  <p>Following data comes from the book "<a href="http://people.cs.ubc.ca/~murphyk/MLbook/" rel="nofollow noreferrer">Machine Learning - A Probabilistic Perspective</a> (Figure_1)"</p>
  
  <p><a href="https://i.sstatic.net/ZoStG.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZoStG.png" alt="enter image description here"></a></p>
  
  <p>here is the corresponding <a href="https://bioinformatics.stackexchange.com/a/9089/4962">sequence logo</a> (Figure_2).</p>
  
  <p><a href="https://i.sstatic.net/3jR8j.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/3jR8j.png" alt="enter image description here"></a></p>
  
  <p>ten rows represent sequences of DNA (e.g. row 1 could be a human sequence, row 2 could be the equivalent mouse sequence etc.)</p>
  
  <p>Each column corresponds to a particular position.</p>
  
  <p>Why do ten rows (Figure_1) correspond to 2 bits (Figure_2)?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-07-29T15:37:03.893Z
Comments.Text: You can find on e.g., [wiki](https://en.wikipedia.org/wiki/Sequence_logo) how a sequence logo is created.
Comments.UserDisplayName: benn
Tags: <phylogenetics><ngs><sequence-analysis>
Title: Why do ten rows (Figure_1) correspond to 2 bits (Figure_2) in a sequence logo?
ThreadText: # Why do ten rows (Figure_1) correspond to 2 bits (Figure_2) in a sequence logo?
  
  (Asked by: username_0 on 2019-07-29)
  
  Following [this question](https://bioinformatics.stackexchange.com/questions/9087/what-is-aligned-sequences-and-consensus-sequence-in-the-context-of-sequence), I'm confused with the [computation of sequence logo](https://en.wikipedia.org/wiki/Sequence_logo)
  
  Following data comes from the book "[Machine Learning - A Probabilistic Perspective](http://people.cs.ubc.ca/~murphyk/MLbook/) (Figure\_1)"
  
  [![enter image description here](https://i.sstatic.net/ZoStG.png)](https://i.sstatic.net/ZoStG.png)
  
  here is the corresponding [sequence logo](https://bioinformatics.stackexchange.com/a/9089/4962) (Figure\_2).
  
  [![enter image description here](https://i.sstatic.net/3jR8j.png)](https://i.sstatic.net/3jR8j.png)
  
  ten rows represent sequences of DNA (e.g. row 1 could be a human sequence, row 2 could be the equivalent mouse sequence etc.)
  
  Each column corresponds to a particular position.
  
  Why do ten rows (Figure\_1) correspond to 2 bits (Figure\_2)?
  
  **Tags:** phylogenetics, ngs, sequence-analysis
  
  > **Comments:**
  > **username_1**: You can find on e.g., [wiki](https://en.wikipedia.org/wiki/Sequence_logo) how a sequence logo is created.  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_2 on 2019-07-29. Score: 6 | Accepted answer
  
  Bits are not frequencies. If a position only contains an A (position 3 for example) then you would need 2 questions (bits) to derive that information without a priori knowledge.
  
  1. Is it a G or C? if no > then it is a A or T
  2. Is it T? If no then it is an A
  
  Position 1 can be derived by 1 question only:
  
  1. is it a G or C? If no then it is an A or T
  
  In this case the number of bits can be calculated using the frequenci)es.
  
  **For 4 bases, A only (100%)**:
  
  4 \* -0.25 \* log2(0.25) - (-1 \* log2(1)) = 2 (bits)
  
  **For 8 letters, A only (100%)**:
  
  8 \* -1/8 \* log(1/8)- (-1 \* log2(1)) = 3 (bits)
  
  **Mixed base possibility (A/T 50% each) with 4 bases**:
  
  4 \* -0.25 \* log2(0.25) - (-0.5 \* log2(0.5)+-0.5 \* log2(0.5)) = 1 (bit)
  
  As mentioned in the comments, you can follow the wiki link for an example.
  
  Or, an example with a little more explanation from the biology SE site.
  
  [sequence logo calcuation](https://biology.stackexchange.com/questions/64368/how-to-determine-the-height-bits-in-a-sequence-logo)
  
  Hopes this helps
  
  > **Comments:**
  > **username_0**: Thanks for your answer. In this specific case, `4 bases` is being used, since there are a,t,g,c 4 Nucleotides in total, right?  
  > **username_2**: correct. That is this part: 4 * -0.25 * log2(0.25) of the equation.  
  
  ---
  
  