Counting sequences

The runs are first listed in standard order (i.e., a binary counting sequence, least significant bit on the right) ... 

Examples of applications of the rules to obtain uniform length descriptors are - EVA descriptors, - topological charge indices, atomic walk count sequence, -+ SE-vectors, - molecular profiles, -> 3D-MoRSE descriptors, - autocorrelation descriptors. 

This implies at least one rule to define a fixed number L of elements in each vector and one rule to fill in the vector elements when the values are missing (for example, filling in with zero values). Examples of uniform-length descriptors are EVA descriptors, topolcgical charge indices, atomic walk count sequence, —> SE-vectors, molecular profiles, spectra descriptors, 3D-MoRSE descriptors, autocorrelation descriptors, affinity fingerprints, and most of the string... 

The neutron activation analysis was carried out at Livermore s 3-megawatt reactor. High resolution lithium-drifted germanium detectors were used to count the samples. Details of the irradiation and counting sequence can be found in an earlier paper (6). 

Since we are accustomed to thinking in terms of the decimal (base 10) number system, decade counters are often used in interface systems. They not only count in powers of 10 but can be used to divide clock frequencies in decade rather than binary steps. The decade counter presented in Figure 23.20, along with its timing chart, follows the count sequence presented in Table 23.7. The BCD Binary Coded Decimal) number system is a binary representation of the decimal number system. 

Unlike asynchronous counters, in which the output change of one flip-flop is applied to the clock input and thus changes the state of a succeeding flip-flop, synchronous-counter flip-flop outputs set up the J and K inputs of succeeding flip-flops so that a common clock-signal can cause the proper count sequence to occur. 

A synchronous binary up-counter is illustrated in Figure 23.21A. Compare this counter with the asynchronous binary up-counter in Figure 23.19. Notice that the synchronous counter requires external gating whereas the asynchronous counter does not this is because the count sequence is generated by the external gates which set up the J and K inputs of each flip-flop. The timing chart in Figure 23.19B for the asynchronous binary counter can also be used for the synchronous counter. 

The question arises, why one would use the more complex synchronous counters rather than the simple asynchronous counters One important reason is that in asynchronous counters the various count sequences must ripple from one flip-flop to the next. This means that an incoming count on the first flip-flop, which will... 

MOVI (moving inversion) This test checks for address propagation failures. It is similar to a march but in addition uses each address Hne as the least significant bit in a counting sequence. 

EXAMPLE 1.13 Counting sequences of distinguishable and indistinguishable objects. How many different arrangements are there of the letters A, H, tmd A That depends on whether or not you can tell the A s apart. Suppose first that one A has a subscript 1 and the other has a subscript 2 Aj, H, and A. Then all the characters are distinguishable, as in Examples 1.11 and 1.12, and there are W = N = 3 = 6 different arrangements of these three distinguishable characters ... 

EXAMPLE 1.15 Counting sequences of coin flips and die rolls. You flip a coin N = 4 times. How many different sequences have three heads According to Equation (1.19),... 

Knowing the mass, density and reaction cross section of the foil material, and the efficiency of the counting system, the neutron flux, nv, can be derived. Corrections, of course, have to be made for decay of the foil activity during any time lapse between removal from the reactor and start of the counting sequence. 

On a slightly more sophisticated level, we can analyze this 10-unit segment by counting sequences two at a time, that is, counting the number of dyads (2-ads) in the chain. The final AA dyad arises because the adjacent segment that is identical to this segment starts with A. There are four possible types of dyads, AA, BB, AB, and BA, and for this chain... 

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