This is also how high quality electronic motor drives and servos generally work.
Switched power supplies have always seemed to be, to me, kin to class D amplifiers, though the block diagrams don't highlight the similarities.
Well, they also put a low-pass filter after.
My (effectively one-line) implementation above was derived from first-principle:
Given a desired target level 0 <= T <= 1, control the output O in {1,0}, such that O on on average is T. Do this by integrating the error T - O over time and switching O such that the sum of (T - O) is finite.
S = O = 0
loop:
S = S + (T - O)
O = (S >= 0)
S = O = 0
loop:
D = T + (~O + 1) << N === T + (O << N) + (O << (N+1))
S = S + D
O = 1 & ~(S >> (N+1))
Another example is Bresenham's algorithm for drawing straight lines on raster displays. The quantity being approximated there is the slope of the line, which is approximated with minimal diffused error as the line is being drawn with only integer adds and subtracts. No divisions and no floating point needed.
These are some of the most subtly beautiful algorithms in computing.
module pdm(clk, level, O);
parameter N = 16;
input wire clk;
input wire [N-1:0] level;
output wire O;
reg [N+1:0] sigma = 0;
assign O = ~sigma[N+1];
always @(posedge clk) sigma <= sigma + {O,O,level};
endmodule
There are some fun techniques in the article, though! I was surprised to see my friend Norm Hardy mentioned — I had never realized he was a pioneer of computer music :)
By the way, while the principle behind class D amplifiers was already long known, it's the gallium nitride MOSFET technology used for switching that makes them really of sufficient quality.