'Negabinary' (radix -2) is a fairly obscure numeral system used in the experimental Poland computers SKRZAT 1[?] and BINEG[?] in 1950.
Numbers can be convered to negabinary by repeated division by -2, recording the remainder of 0 or 1.
To add two negabinary numbers, start with a carry of 0, and, starting from the least significant bits[?], add the bit of each number plus the carry, record the bit of the resulting number and set the carry according to the number.
and is represented by 10001 in binary and 10001 in negabinary.
The negabinary expansion of a number can be found by repeated division by -2, recording the non-negative remainders of 0 or 1, and concatenating those remainders, starting with the last.
Note that the negabinary expansions of negative integers have an even number of bits, while the negabinary expansions of the non-negative integers have an odd number of bits.
'Negabinary' (radix -2) is a non-standard positional numeral system used in the experimental Polish computers SKRZAT 1 and BINEG in 1950.
and is represented by 10001 in binary and 10001 in negabinary.
The negabinary expansion of a number can be found by repeated division by -2, recording the non-negative remainders of 0 or 1, and concatenating those remainders, starting with the last.
The negabinary representation of a number n is given by the coefficients
The following table gives the negabinary representations for the first few integers (A039724).
The numbers having the same representation in binary and negabinary are members of the Moser-de Bruijn sequence, 0, 1, 4, 5, 16, 17, 20, 21, 64, 65, 68, 69, 80, 81,...
At 7 pm on 21 October 1999, participants in the 1999 Mathematica Developer conference were challenged to construct a function which can calculate the negabinary representation of any integer (see below).
A number is found from its negabinary representation by adding together the corresponding powers of negative two.
Knowing this, it is easy to write a function that finds an integer, given its negabinary representation.
The ``Logical Alternative to the Existing Positional Number System'' by Robert R. Forslund discusses using the digits 1 to b instead of 0 to (b-1) for a given base b.
The negabinary system is base -2; it appears that this system was used by the experimental Polish computers SKRZAT 1 and BINEG in 1950.
In Negabinary, negative and positive numbers can be represented without a sign bit, and arithmetic operations are more complicated.
Based on the negabinary number representation, parallel one-step arithmetic operations (that is, addition and subtraction), logical operations, and matrix-vector multiplication on data have been optically implemented, by use of a two-dimensional spatial-encoding technique.
For addition and subtraction, one of the operands in decimal form is converted into the unsigned negabinary form, whereas the other decimal number is represented in the signed negabinary form.
The result of operation is obtained in the mixed negabinary form and is converted back into decimal.
Kuwait Journal of Science & Engineering(Site not responding. Last check: )
More efficient one-step negabinary signed-digit algorithms for the addition/subtraction operations are proposed.
To increase the information storage density high-radix (trinary with radix = -3 and quaternary with radix = -4) negabinary signed-digits are employed.
It is shown that by using digits grouping of the negabinary signed-digits, a huge reduction of the number of the symbolic substitution computation rules involved in the arithmetic computations will be achieved.
Wavelet transforms are very effective for analysing the information content of a signal, so how to implement wavelet transforms efficiently becomes a vital task.
In this paper, we propose a novel negabinary encoded digital matrix - vector multiplication and an incoherent optical correlator to carry out discrete wavelet transforms.
The method has the properties of parallelism, high efficiency and being easy to establish.
No part of this database may be downloaded, reproduced, or distributed in any form, or by any means, or stored in or transferred to any other database or retrieval system for commercial purposes or for access by multiple users without written permission from SPIE.
Negabinary is a component of the positional number system.
A complete set of negabinary arithmetic operations are presented, including the basic addition/subtraction logic, the two-step carry-free addition/subtraction algorithm based on negabinary signed-digit (NSD) representation, parallel multiplication, and the fast conversion from NSD to the normal negabinary in the carry-look-ahead mode.
Books Album: Free E-Books Collection. All are new books of latest edition(Site not responding. Last check: )
The digits used are 0 and 1, as in base +2; that is, the value represented by a string of 1's and 0's is understood to be
From this, it can be seen that a procedure for finding the base -2, or "negabinary," representation of an integer is to successively divide the number by -2, recording the remainders.
The division must be such that it always gives a remainder of 0 or 1 (the digits to be used); that is, it must be modulus division.
As with any other bases, the weight of position i is b^i, so the positions for an 8-bit negabinary number are:...
Formats: (u) unsigned binary (s) sign/mag binary (1) 1s complement (2) 2s complement (n) negabinary (d) decimalinteger Use getc and putc for all the [nega]binary bases.
Feel free to post negabinary conversions on the newsgroup to see if they're correct.
Base -2, for example, is a system in which both positive and negative numbers can be represented without using an explicit sign bit.
As in the more familiar binary system, negabinary numbers are represented by 0/1 bits -- but the sign flips in every other digit.
The advantage of negabinary numbers is their simplicity in representing negative numbers, but their downside is that negabinary arithmetic operations such as division are quite complicated.
Nitendra Rajput(Site not responding. Last check: )
This was followed by my entry into the Government Engineering College, Jabalpur, where I did my Bachelor's degree in Electronics and Telecommunications Engineering.
In the final year of graduation, I did the project work on design of some Negabinary Circuits.
This involved exploring Negabinay as the number system to implement the digital circuits like Adders, Subtractors, Counters, etc. I completed my degree in 1996 and then moved to Indian Institute of Technology, Bombay for Masters.
