In theory for this project you may use one IC 4 bit binary full adder and one IC quadruple 3 lines to 1 line multiplexer. The result of the multiplexer to be applied to a BCD to 7 segment decoder and address multiplexing to be implemented with push buttons.
In practice we may use for example two IC dual 4-line to 1-line multiplexer (SN74153). The push buttons and some diodes must be connected generate the three needed addresses: 00, 01, 10.
MUX binary input address 00 = selection of A input
MUX binary input address 01 = selection of B input
MUX binary input address 10 = selection of result
4 bit binary full adder = SN7483
BCD to 7 segment decoder = SN7447
If none of the buttons pressed then the output of MUX= 0000.
See the diagram attached:
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