It is shown that A/D conversion to base –2 may be achieved by making minor modifications to a conventional A/D converter.

A method for the direct conversion of multilevel values to their Gray code representations is presented. This eliminates the need for binary-to-Gray code conversion. The method is particularly suited for parallel implementation.

Contains an introduction and reports on twenty research projects.

It is shown that Little's algorithm for high-speed digital filters can be applied to data represented in two's complement form. It is not necessary to use the more complex "biased" form or negative base representation.

A new representation for decimal numbers is proposed. It uses a mixture of positive and negative radixes to ensure that the maximum value of a four bit decimal digit is 9. This eliminates the more complex carry generation process required in BCD addition.

Summary form only give, as follows. Bauer is quite correct in pointing out that the use of unnormalized floating point format improves the overall accuracy of the representation. It is therefore intriguing to ask why more manufacturers have not adopted it. Presumably most designers prefer to keep floating point number representations unique. In some computers the leading bit of each mantissa is dropped when the floating point number is stored in core, but added back when the number IS sent to the arithmetic u~it or an output unit. To do this one must assume that the leading bit of each mantissa is 1, i.e., normalized form. Whether one places the radix point to the left or the right of the mantissa does not affect the advantages or disadvantages of the integrated representation: we are merely altering all the numbers and all the rounding errors by a factor of 2m.

I am grateful to D. P. Agrawal for his enlightening comments, and take the opportunity to add the following remarks for general interest

A new, revised edition of a yet unrivaled work on frequency domain analysis Long recognized for his unique focus on frequency domain methods for the analysis of time series data as well as for his applied, easy-to-understand approach, Peter Bloomfield brings his well-known 1976 work thoroughly up to date. With a minimum of mathematics and an engaging, highly rewarding style, Bloomfield provides in-depth discussions of harmonic regression, harmonic analysis, complex demodulation, and spectrum analysis. All methods are clearly illustrated using examples of specific data sets, while ample

In the above paper1Edwards shows the implementation of several Boolean functions using a threshold gate and XOR gates. An unstated, but implicit, result is that any given Boolean function can be synthesized in this way. This result is of some historical interest. We wish to relate it to a previous paper by Kaplan and Winder [1], which in effect derived the result, and then to a mathematical study of Lawson [2], [3], which yields a synthesis procedure with very general applicability.

It is shown that the cyclic correlation between two Walsh functions is identically zero except if they have equal "Contradegrees."

It is shown that arithmetic operations are simplified if complex numbers are represented in an integrated form with real and imaginary parts sharing the same exponent. In the new representation, numbers with large magnitudes suffer increased rounding errors but errors for some other numbers decrease.

A scheme for computing the Walsh-Fourier transform of noisy data is presented. The results are insensitive to isolated noise points, even when their magnitudes are large.

Circuits for performing arithmetic operations using base –2 representations are considered. Study of the counting process leads to a negative binary up-down counter and new simple methods for positive-negative base conversions. The advantage of employing carry-borrow rather than carry-only during additions is pointed out. Certain special features of negation, arithmetic shift, multiplication, and division in base –2 are described.

Interchannel interference in multiplexing systems using Walsh-function carriers is considered. In such systems excessive sequency bandwidth of input signals or synchronization errors destroy orthogonality between received signals and demodulating functions, causing crosstalk. The former cause is studied using Yuen's integration-by-parts method, while for the latter correlation of Walsh functions is derived. For both causes crosstalk is small ff a "weighted distance" between the indices of the two channels is large.

It is proved that, when binary strings are Gray coded into multilevel signals, to cause an error ofmbits, the multilevel signal must have an error of more than2^m /3. This generalizes the well-known result that a one-level error in the signal generates only a one-bit error in the binary string.

Operations of the Chinese abacus in arithmetic computation follow a set of rules for moving beads. Such rules are memorized and followed by the operator to carry out computation rapidly even if he is mathematically untrained. In this correspondence, these rules, in terms familiar to the western reader, are discussed. Some problems inherent in the abacuis are also pointed out.