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. Matrix–vector multiplication for unsigned negabinary numbers is achieved through the convolution technique. Both of the operands for logical operation are converted to their signed negabinary forms. All operations are implemented by use of a unique optical architecture. The use of a single liquid-crystal–display panel to spatially encode the input data, operational kernels, and decoding masks have simplified the architecture as well as reduced the cost and complexity. © 2002 Optical Society of America.