This is a very tangential. I did some work in Trinary computer emulation a lifetime ago, there's a cute trick for finding a closed form translation between a division by a power of 3, and series of bit shifts and additions.
Start by observing that
1/3 - 1/2 = 2/6 - 3/6
or
1/3 = 1/2 - 1/2 (1/3)
Substitute equation above into RHS an infinite number of times and find
1/3 = -(-1/2)^N for N in 1..inf
You can do this with arbitrary pairs powers of 2 and 3 (also other bases).
The implication is that you can fairly easily build a fixed time divide-by-constant circuit as out of nothing but adders and subtractors for values that are close to a power of two.
Incredible, thanks for sharing. My understanding is that ternary computers would have been based on tri-state logic which was less reliable than say transistors or even vacuum tubes encoding binary state. Is that understanding correct?
Start by observing that
1/3 - 1/2 = 2/6 - 3/6
or
1/3 = 1/2 - 1/2 (1/3)
Substitute equation above into RHS an infinite number of times and find
1/3 = -(-1/2)^N for N in 1..inf
You can do this with arbitrary pairs powers of 2 and 3 (also other bases).
The implication is that you can fairly easily build a fixed time divide-by-constant circuit as out of nothing but adders and subtractors for values that are close to a power of two.