Owing to their form, 2 < sup > p − 1 </ sup >( 2 < sup > p </ sup >− 1 ), every even perfect number is represented in binary as p ones followed by p − 1 zeros:

This is because, for a perfect case, each intersection test would divide the possibilities by two, and we would have a binary tree type structure.

The only nontrivial and useful perfect codes are the distance-3 Hamming codes with parameters satisfying ( 2 < sup > r </ sub > – 1, 2 < sup > r </ sub > – 1 – r, 3 ), and the binary and ternary Golay codes.

The other, the perfect binary Golay code, has codewords of length 23 and is obtained from the extended binary Golay code by deleting one coordinate position ( conversely, the extended binary Golay code is obtained from the perfect binary Golay code by adding a parity bit ).

The perfect binary Golay code is a perfect code.

The codewords in the perfect ( non-extended ) binary Golay code are of size 23.

Tree rotations are very common internal operations on Self-balancing binary search tree | self-balancing binary trees to keep perfect or near-to-perfect balance.

* Bitstream processing ( Context-adaptive variable-length coding / Context-adaptive binary arithmetic coding ) and perfect pixel positioning.

** In binary, all even perfect numbers are Kaprekar numbers.

* Generalization of the perfect binary Hamming codes to non-binary codes.

* The Key To The Universe ( previously Numbers: The Key To The Universe, ISBN 0-439-98116-6 ( Fibonacci Series, Golden Ratio, properties of Square, Triangle, Cube, Centred Hexagon and Tetrahedral numbers, " difference of two squares ", number superstitions, prime numbers, Mersenne primes, tests to see if a number will divide by anything from 2-13 and 19, finger multiplication, binary and base 8, perfect numbers, irrational transcendental and imaginary numbers, infinity.

In terms of binary representation of the PEs, each stage of the perfect shuffle can be thought of as a cyclic logical left shift ; each bit in the address is shifted once to the left, with the most significant bit moving to the least significant bit.

If one assumed that all the data being read and written was a decimal representation of binary data the system made perfect sense, but if the data was in some other form, more complex assembler language character codes for instance, it ended up simply added complexity that then had to be turned off.

His structures echo natural forms, with columns like tree trunks supporting branching vaulting under the roadway, and the curves of vaulting and alignment of sloping columns designed in a similar way to his Church of Colònia Güell so that the inverted catenary arch shapes form perfect compression structures.

Sometimes a full tree is ambiguously defined as a perfect tree.

Mazes containing no loops are known as " standard ", or " perfect " mazes, and are equivalent to a tree in graph theory.

The Christofides algorithm follows a similar outline but combines the minimum spanning tree with a solution of another problem, minimum-weight perfect matching.

The technique is not perfect, as freeze-thaw cycles ( in cold-weather regions ) and tree root growth can eventually result in damage which requires repair.

Although the flowering is dioecious, the pistillate tree even when isolated will bear large oranges, perfect to the sight but lacking the seeds.

The tree is hermaphroditic, having perfect flowers, ( i. e. with both male and female parts ) and is therefore capable of self-pollination.

The Golden Delicious ' long keeping qualities were soon abundantly evident to Mr. Stark, as well as to United States Pomologist Colonel Brackett, in Washington, and the nursery bought the tree and ground on which it stands from Mr. Mullins for the-then-golden sum of $ 5, 000. 00, after verifying that the tree was the producer of the long sought perfect yellow apple.

Visitors to the refuge can walk, bike, drive, or kayak though the wildlife drive which takes you through five miles ( 8 km ) of mangrove tree forests and tidal flats, this drive is perfect for watching the island's wildlife and looking at the island's native vegetation.

The American Forestry Association proclaimed the tree as the most perfect specimen of a North American tree, and inducted the Treaty Oak into its Hall of Fame in Washington, D. C.

In game theory terms, an expectiminimax tree is the game tree of an extensive-form game of perfect, but incomplete information.

* A perfect k-ary tree is a full k-ary tree in which all leaf nodes are at the same depth.

And it is expressed, at least to their taste, in a perfect form.

Admirably written, it is a perfect introduction to Swedish history for readers of other countries.

By virtue of his self-reliance, his individualism and his freedom from external restraint, the private eye is a perfect embodiment of the middle class conception of liberty, which amounts to doing what you please and let the devil take the hindmost.

Now what is perfect motion??

Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

I assume that the number of readers of this anthology who regard themselves as morally perfect is small, and that most readers are willing to consider procedures by which they may gain more insight into themselves and better understanding of others.

Here is truly a `` Great Recording of the Century '', and its greatness is by no means diminished by the fact that it is not quite perfect.

Yet you feel the orchestra is near at hand, and the individual instruments have the same firm presence associated with listening from a good seat in an acoustically perfect hall.

Probably no location for a pool is perfect on all counts.

The way in which it transports its pollen is not so perfect, either.

Second, if there is ever a perfect time to pull the rug out from under him, it's on maneuvers.

Its rotunda forms a perfect circle whose diameter is equal to the height from the floor to the ceiling.

It is hard, on the other hand, to blame the policeman, blank, good-natured, thoughtless, and insuperably innocent, for being such a perfect representative of the people he serves.

This acquisition is a matched, perfect set -- consisting of two sofas six feet long, plus six sidechairs and two armchairs.

Looking unto God, the Prophet Isaiah wrote these blessed words almost three thousand years ago: `` Thou wilt keep him in perfect peace, whose mind is stayed on thee: because he trusteth in thee ''.

That is almost a perfect description of the predicament in which we find ourselves today, isn't it??

Mr. Foy is a joy, having learned his dancing by practicing it until he is practically perfect.

Being a dimensionless fraction, it may also be expressed as a percentage, and is measured on a scale from zero for no reflecting power of a perfectly black surface, to 1 for perfect reflection of a white surface.

Algerian music is a perfect reflection of the cultural diversity that characterizes the country, music directories are distinguished by a profusion of several styles.

Therefore the perfect of these verbs would be ich bin gesessen, ich bin gelegen and ich bin geschlafen respectively ( note: ich bin geschlafen is a very rare form, usually you will hear ich habe geschlafen ; but ich bin eingeschlafen fell asleep is quite normal ).

In the variant of German that is spoken in Germany, the words stehen ( to stand ) and gestehen ( to confess ) are identical in the present perfect: habe gestanden.