Combinations of binary digits for decimal numbers

I can think of three ways to do this. I'll start from the most expensive and complicated and work my way down.

1. All Logic IC's: Use a parallel-load 9-bit up/down binary counter (such as 3x 74hc190) and a 3-digit resettable BCD counter (3x 74hc163). Load the binary counter with your 9-bit number, and clear the BCD counter to 0. Clock both counters until the binary counter reaches zero. Load the output of the BCD counter into a latch, and then feed it to a BCD-7seg decoder. Repeat.
   • Pros:
     • Meets requirement of only using standard logic IC's
     • Requires no programming
   • Cons:
     • Expensive (The counter chips are about $1-2 each)
     • Prone to wiring failure
     • Requires a clock signal of 31kHz for 60Hz refresh
     • Requires 8-12 Logic IC's (I'll draw a schematic later)
       
       
2. ROM Look-Up Table: Use a small parallel asynchronous FLASH memory (such as this one) to take all data inputs as an address, and then program the ROM to generate BCD outputs for 2 digits. Feed the result into a BCD-to-7seg decoder. Alternatively, use one ROM to generate a single decimal digit decoded into 7-segment pins.
   • Pros:
     • Fairly cheap price per digit
     • Scales better
     • Fast (but speed doesn't really matter)
     • Simple to wire/design
   • Cons:
     • Each ROM requires different programming
     • Need to buy a much larger ROM than needed
     • Programming requires computer automation.
       
       
3. Microcontroller: A simple microcontroller with enough inputs and outputs can convert the binary number into BCD, and then encode it into 7-segment control signals. The cheapest solution (My digikey search picked out this PIC) will multiplex the output digits. You may need transistors to drive the common anode/cathode of your 7-segment displays, but those can be cheap transistors.
   • Pros:
     • The cheapest solution at $1.50 - $2.00 total
     • Simple Wiring
     • Ease of implementing Binary->BCD algorithm in software
     • Easy to add more functionality
     • Least expensive system for driving the display
   • Cons:
     • A chip programmer is required
     • You need to write software (not just a hardware problem)
     • The cheapest solution requires digit multiplexing, which is more complicated than direct drive.
       

I'll draw up some schematics later

If you want to add two N-bit numbers, a parallel adder will use N copies of a full-adder circuit, and it will produce a result in one clock cycle.

On the other hand, a serial adder will use just one full-adder circuit, but it will require N clocks to produce the result.

The tradeoff is circuit complexity (and power consumption) vs. time.

Some examples: A desktop PC uses a parallel adder, because it wants to be able to do as much arithmetic as possible in a given amount of time, and there is no real restriction on how much power it can consume. On the other hand, a handheld calculator only needs to be as fast as the human operating it, but it needs to last a long time on a small battery, so it uses a serial adder.