Actually, Engineering Research Associates (predecessor of Univac) built a CPU with mercury delay line memory using acoustic transducers to create a shift regist

Actually, Engineering Research Associates (predecessor of Univac) built a CPU with mercury delay line memory using acoustic transducers to create a shift register. It did bit-serial binary arithmetic. You could get two logic gates or one latch out of a dual pentode, so a bit-serial ALU could fit easily in a single rack. I'm not familiar with the overall architecture, though, unfortunately. I do remember having to do a most-significant-bit first, bit-serial, two's complement adder as a homework assignment that was inspire by the machine.