Using the 4094, the clock needs to be a steady repetitive signal, also as shown in your schematic the input pins are all tied directly to the +5.0V line–this keeps them high regardless of how you set the K8055 outputs.
However, to start from the beginning, you first will need an external +5.0V power source as the K8055 ADC output cannot supply sufficient current to power all 8 LEDs,
Here’s a schematic using a 74HC4094, just one output is shown for simplicity:
Resistors R1…R4 are pull-up resistors needed to keep the 4094 inputs high when the K8055 output is “high” (or actually not low, as it is an open collector output).
The K8055 outputs are as follows:
[ol][li] 74HC4094 enable;[/li]
[li]74HC4094 data strobe;[/li]
To utilise this, the process would be as follows:
[li]Bring K8055 output 2 high to enable the input strobe;[/li]
[li]Set the desired data bit on K8055 output 3;[/li]
[li]Toggle the K8055 output 4 high then low to record the data and shift the registers;[/li]
[li]Bring K8055 output 1 high as desired to enable the outputs;[/li][/ol]
Bringing output 2 (strobe) low would lock the state of the outputs.
It is important that the output data be supplied in synchronization with the clock, as any data transitions that occur between the clock’s rising pulse, and high/low/high (or low/high/low) data transition that occurs withing one clock cycle will not be brought into the shift register.
I believe this makes the '4094, and any synchronous shift register, a hassle to use for what it appears you wish to do. Although it might be possible to use the clock signal asynchronously to toggle the
Note: Referring to the 74HC164 partial schematic I posted earlier, you would also need the external power source and the pull-up resistors–used in a similar manner to what is shown above.