I know the circuit well I did several of them Many years ago... The "Clock is the rate at which the data moves through those logic IC's. They weren't static. Your '285 takes 2 4 bit binary words and "Adds them together... although it is a parallel process it Still was "Clocked Logic"... There is a specific rate at which the data moves through the adder... That is the clock rate. TTL was also famous for it's quiescent current and when you produce a chip of that complexity there's a lot of gates drawing power... They get even hotter when you run them fast... BTW LS means "Low Power Schottky" which was about as fast as "regular" 7400 series logic and drew about 1/10th the power and there were ECL logic chips that could ruin your whole day... If you touched them... kind of a circle because ECL and things like USB are Very similar in theory/technology as ECL was the fore runner of what is called LVDS or "Low Voltage Differential Signalling". The theory is that it doesn't take as much power (heat) to move a pair of wires about a common LOW center voltage as it does to take one conductor and slam it between Vcc and ground as fast as you can as for one.. the parasitic capacitance's aren't as big so it doesn't take as much energy (heat) to charge and discharge them. Does this help?
I am not sure that it helps but it is very interesting and useful information in a general way. As far as my circuit goes, I guess I should just expect those 8 ICs to run hot. I can live with that as long as it is not damaging them and so far, no problems. Not like I wanted to run that circuit 24/7 inside a computer anyway, I just wanted to wire it to prove to myself that I could do it and it works. What it does is takes two 8 bit values and multiplies them a nybble at a time. Byte 1 is nybbles A,B, Byte 2 is nybbles C,D. The four multiplier pairs multiple AC, AD, BC, and BD and the other chips basically sum those partial products (utilizing carry lookahead to keep it as fast as possible), just like you would on paper but in octal rather than decimal. It's a cool circuit.