Arithmetic circuits

Giuliano Donzellini, Domenico Ponta, Davide Anguita

Design of a sign converter




Design a digital circuit that converts a signed, positive, three-bit number to the corresponding negative number, using two’s complement representation (e.g. +2 = '010' becomes -2 = '110'). In2 and Out2 are the sign bits.

The network checks if the input number is already negative and, in this case, it activates an error signal (Neg = '1') and copies (without changes) the input number to its outputs.

Write a truth table of the converter. Compile a K-maps for each output and write the expressions of the minimized synthesis of each output (synthesize them as two-level AND-OR networks).

Draw the schematic of the resulting network, using (as a trace for the solution) the d-DcS schematic template provided here (click on the figure below).

Verify the circuit behaviour through a functional simulation and a timing simulation (a suitable test sequence is available in the Timing Diagram window).