How does a BCD to seven-segment decoder work?

A BCD to seven-segment decoder converts 4-bit Binary Coded Decimal input (0-9) to outputs that drive the seven segments (a-g) of a display. Each segment is controlled by a Boolean function of the BCD inputs. For example, segment 'a' is ON for digits 0,2,3,5,6,7,8,9. The 7447 (common anode) and 7448 (common cathode) are standard ICs. Invalid BCD inputs (10-15) either blank the display or show unique patterns depending on the decoder design.