Unified negabinary symbolic arithmetic for addition and subtraction with polarization-encoded optical shadow casting

A parallel optical implementation of arithmetic operations

“…In optical shadow casting, the light emitted by an array of light emitting diodes passes through a few input planes and then forms an overlapped pattern on the output plane [2]. Optical shadow casting was used to implement addition [4,10], and was augmented to use the modified signed-digit number system [59] to perform addition more efficiently [7,15,16].…”

“…Diversity of supported operations: Almost all of the past optical processors implement a single arithmetic operations like addition [14,15,23,35,36,53,63], multiplication [70], or vector-matrix multiplication [29,38,39]. In this paper we implement different arithmetic operations, making it possible to perform various multi-step computational tasks.…”

“…In fact, the studies for using optics for computing began more than five decades ago [1]. Especially in years 1980-1995, a large number of researchers invested in optical computing and presented several techniques to use optics in parallel processing, such as optical shadow casting [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], optical symbolic substitution [18][19][20][21][22][23][24], and optical vector-matrix multiplication [1,[25][26][27][28][29][30][31]. After this golden age of optical computing, it experienced a slowdown near the end of the last millennium.…”

<title>Efficient optical negabinary signed-digit arithmetic operations and implementation using electron-trapping device</title>

“…output "1": h +(a1 b)g,f , (2) for t, outputl": (ab1 +(a b)fg , (3) output"l': (a 'b. )f , (4) forw1, output"l": (ab)f. (5) In the second step, the involved logic operations for the final sum s are the same as for w in the first step by defining a binary reference bit g which is true for nonnegative t and w.…”