In a previous paper it was shown that reducing the amount of glitches in digital designs can significantly reduce the amount of dynamic power consumption. Pipelined multipliers and a bit-serial multiplier design were used to show this. The paper failed to mention how much of the dynamic power consumption was due to the clock distribution. Also the only digitserial multiplier digit size investig...

We show how to apply the Collatz function and the modified Collatz function to the ternary representation of a positive integer, and we present the ternary modified Collatz sequence starting with a multiple of 3N for an arbitrary large integer N . Each ternary string in the sequence is shown to have a repeating string, and the number of occurrences of each digit in each repeating string is iden...

This paper presents a novel number system based on signed continuous valued digits. Arithmetic operations in this number system are performed using simple analog circuitry, in contrast to the conventional implementation of arithmetic units by Boolean or multiple-valued logic circuits. Unlike the limited precision offered by classical analog arithmetic circuits, the ensemble of continuous valued...

This paper investigates "what's in a number", i.e. how natural numbers are pronounced in several European languages. As regards reading numbers above 20, 29 languages read the decade first and then the digit, e.g. twenty-four, and 10 languages read the digit before the decade, e.g. four-and-twenty. Two languages, Norwegian and Czech, use both systems, and 9 languages use (partly) a vigesimal sy...

The purpose of this master's thesis was to explore the circuit design space (speed, area, power) of conventional binary arithmetic and to suggest improvements or alternatives to this arithmetic. The alternatives to the binary arithmetic focused on was the Signed-Digit (SD) number system, the Residue Number System (RNS) and the combination of these two systems (RNS+SD). The work resulted in new ...

Oliver Sacks published an extremely influential book, The Man Who Mistook His Wife For A Hat, in 1985. One of the most intriguing stories in it is concerned with savant syndrome, which refers to the exceptionally high abilities shown by otherwise handicapped individuals (e.g., autism). His story is cited in many journal articles as well as popular science books. To reiterate, he discovered that...

Define a k to be the smallest positive multiple of k such that the sum of its digits in base q is equal to k. The asymptotic behavior, lower and upper bound estimates of a k are investigated. A characterization of the minimality condition is also considered. A positive integer n is a Niven number (or a Harshad number) if it is divisible by the sum of its (decimal) digits. For instance, 2007 is ...