The name " bit shift map " arises because, if the value of an iterate is written in binary notation, the next iterate is obtained by shifting the binary point one bit to the right, and if the bit to the left of the new binary point is a " one ", replacing it with a zero.
12.
The name " bit shift map " arises because, if the value of an iterate is written in binary notation, the next iterate is obtained by shifting the binary point one bit to the right, and if the bit to the left of the new binary point is a " one ", replacing it with a zero.
13.
The reason that the dyadic transformation is also called the bit-shift map is that when is written in binary notation, the map moves the binary point one place to the right ( and if the bit to the left of the binary point has become a " 1 ", this " 1 " is changed to a " 0 " ).
14.
The reason that the dyadic transformation is also called the bit-shift map is that when is written in binary notation, the map moves the binary point one place to the right ( and if the bit to the left of the binary point has become a " 1 ", this " 1 " is changed to a " 0 " ).
15.
In the following table, " " s " " is the value of the sign bit ( 0 means positive, 1 means negative ), " " e " " is the value of the exponent field interpreted as a positive integer, and " " m " " is the significand interpreted as a positive binary number where the binary point is located between bits 63 and 62.
16.
The decimal number 0.15625 10 represented in binary is 0.00101 2 ( that is, 1 / 8 + 1 / 32 ) . ( Subscripts indicate the number base . ) Analogous to scientific notation, where numbers are written to have a single non-zero digit to the left of the decimal point, we rewrite this number so it has a single 1 bit to the left of the " binary point ".
17.
Concretely, every binary point group is either the preimage of a point group ( hence denoted 2 " G ", for the point group " G " ), or is an index 2 subgroup of the preimage of a point group which maps ( isomorphically ) onto the point group; in the latter case the full binary group is abstractly \ mathrm { C } _ 2 \ times G ( since { ? } is central ).
18.
This can be seen by noting what the map does when x _ n is expressed in binary notation : It shifts the binary point one place to the right; then, if what appears to the left of the binary point is a " one " it changes all ones to zeroes and vice versa ( with the exception of the final bit " one " in the case of a finite binary expansion ); starting from an irrational number, this process goes on forever without repeating itself.
19.
This can be seen by noting what the map does when x _ n is expressed in binary notation : It shifts the binary point one place to the right; then, if what appears to the left of the binary point is a " one " it changes all ones to zeroes and vice versa ( with the exception of the final bit " one " in the case of a finite binary expansion ); starting from an irrational number, this process goes on forever without repeating itself.
