74LS00 datasheet: NAND gates
74LS02 datasheet: NOR gates
74LS04 datasheet: NOT gates
74LS08 datasheet: AND gates
74LS11 datasheet: 3-input AND gates
74LS32 datasheet: OR gates
74LS83A datasheet: 4-bit adder
74LS85 datasheet: 4-bit comparitors
74LS86 datasheet: XOR gates
74LS138 datasheet: Decoder/demultiplexer
74LS157 datasheet: Multiplexer!
74LS181 datasheet: ALU (Abandon hope all ye who enter here)
74LS191 datasheet: Up/down counter
74LS244 datasheet: Tri-state buffer
74LS273 datasheet: Flip-flop register
28C16A EEPROM datasheet #1 and datasheet #2. These chips have 24 pins.
28C64A EEPROM datasheet: In an ordering snafu, these EEPROM's are quite similar to the ones above, except that they have two additional address bits. You certainly may use them, but be aware that they are somewhat different. These chips, specifically, have 28 pins (instead of the 24 pins of the 28C16A).
A sample mid-term exam and its solutions.
Systems I book [college login required]