title: How to represent negative number in binary
body: <p>I was reading this paragraph on a website and I'm confused as to why <code>100000</code> is equal to -32.</p>
  
  <blockquote>
    <p>One caveat with signed binary numbers is that of overflow, where the answer to an addition or subtraction problem exceeds the magnitude which can be represented with the alloted number of bits. Remember that the place of the sign bit is fixed from the beginning of the problem. With the last example problem, we used five binary bits to represent the magnitude of the number, and the left-most (sixth) bit as the negative-weight, or sign, bit. With five bits to represent magnitude, we have a representation range of 25, or thirty-two integer steps from 0 to maximum. This means that we can represent a number as high as +31 (011111), or as low as -32 (100000).</p>
  </blockquote>
  
  <p>Why does -32 equal 100000. Is that sign magnitude format or 2s complement?</p>