{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}


An even worse choice of representation would be the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: n worse choice of representation would be the following: since 1=10 = (0:00000001100110011 : : :)2 24 the number could be represented by 0 E = 4 0.0000000110011001100110 : This is clearly a bad choice since less of the binary expansion of 1=10 is stored, due to the space wasted by the leading zeros in the signi cand eld. This is the reason why m < 1, i.e. b0 = 0, is not allowed. The only allowable representation for 1=10 uses the fact that 1=10 = (1:100110011 : : :)2 2;4 2 giving the representation 0 E = ;4 1.1001100110011001100110 : This representation includes more of the binary expansion of 1=10 than the others, and is said to be normalized, since b0 = 1, i.e. m > 1. Thus none of the available bits is wasted by storing leading zeros. We can see from this example why the name oating point is used: the binary point of the number 1=10 can be oated to any position in the bitstring we like by choosing the appropriate exponent: the normalized representation, with b0 = 1, is the one which should be always be used when possible. I...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online