The purpose of the integrator and gate circuits is to pass on the number of pulses that match the test voltage being measured. Since a specific pulse frequency stream is being applied to the gate, the test voltage must somehow control how long the gate will be allowed to pass the pulses; the higher the test voltage, the longer the gate will be open, and the more pulses will be passed through- and the number of pulses will represent the digitized version of the analog test voltage.
The test voltage and the gate voltage are combined in the summer (algebraic adder) circuit to produce a gate voltage riding on a dc level. When this is processed by the integrator, the flat top of the gate voltage will be reshaped into a downward slope or ramp waveform, the height and shape of which will depend on the test and gate voltages. The decreasing ramp voltage will initially pass through a level that will trigger the gate open; the gate will stay open until the ramp voltage drops to the level that will close the gate. Between those times, several pulses, corresponding to the test voltage, will pass through the gate to the counter.
The gated pulses recur periodically, about every second or so; a reset signal sets the counter back to zero when a new stream starts. The gated pulses are generally sent through a waveshaper to remove any distortion in the pulse stream and to a counting register to be counted.
The counting registers are binary-coded decimal (BCD) registers. Each register has four flip- flops, each of which can be triggered on and off to indicate a 0 or a 1. The four flip flops can hold 16 different combinations of 0s and 1s but are designed to hold binary codes for digits 0 through 9. Each pulse fed to the 1s (ones) register, resets the flip-flop to raise the digit count by one. When a code count goes from 9 back to 0, a carry pulse is sent to the next higher, or 10s (tens) register. The 10s register will reset its flip-flops once for each 0 to 9 cycle of the ls register. Whenever the 10s register passes through 9, it triggers a carry to the 100s register, and so on.
The four registers here can count 9,999 pulses. Although the next gated sequence of pulses will reset the registers to zero, the counting action is quick, and the only thing that will be noticed is changing digits with a fluctuating test voltage.
Each counter register has four flip-flops, which are turned on and off by the pulses; each flip-flop has an on (flip) and an off (flop) condition. These represent the binary digits (bits) 1 and 0. Four flip flops can represent 16 different combinations of 0 and 1, but only ten are used here for decimal digits 0 through 9. Each of the four flip-flops in each register sends its binary coded decimal number to a BCD decoder, which converts the 0 and 1 bits to decimal digits. Each BCD decoder sends its decimal code to a display driver, which activates the corresponding digit in the display. The actual codes or signals delivered by the display driver depend on the kind of display used.
Sources:
https://www.sciencedirect.com/topics/engineering/digital-circuits
https://learn.sparkfun.com/tutorials/analog-vs-digital/analog-and-digital-circuits
https://www.allaboutcircuits.com/video-tutorials/analog-and-digital-electronics/
