This is a homemade and nicely built training computer, and probably one of the rare computers in the world based on the 1-bit (yes, one bit) Motorola MC14500 processor.
This machine was conceived en sold in Germany by DATANorf Hard and Software in kit or ready-built forms.
Originally, the MC-14500, also called Industrial Control Unit (ICU) was a CMOS processor designed for controlling simple industrial devices and making binary decisions based on successive single bit information. One could find it also in LCD display drivers or as a serial port manager.
It has 16 instructions, including bit transfer, logical single bit comparisons (OR, XOR, AND, NAND), Jump and subroutines. Its internal clock speed started from manual pulses to about 1 MHz.
The pictured computer, made by a German anthusiast, worked when connected to a 9V battery. It includes a LED IO board, CPU board and 512 byte RAM board. The keyboard featured one key for each processor instruction and an octal numeric keypad. Some sounds may be produced through the attached amplifier and loudspeaker.
More information from Kai Ludwig:
The MC-14500 based "WDR-1-Bit-Computer" was invented about 20 years ago as a holiday-project by Burkhard John and Volker Ludwig for educational purposes.
In those days I was running the german company "DATANorf Hard and Software". It sold the "WDR-1-Bit-Computer" as kit. The ciruitboards were homebrew and there were many additional modules available.
Later we made an 6 part educational school-TV-serial with WDR Television and the German company Raffel-Electronics got the licence for professional distibution of the kits with industrial manufactured circuitboards.
Your picture shows a version sold by DataNorf to a home enthusiast. The attached board contains a NE555 oscillator to make a sound. The pitch can be adjusted by the potentiometer.