Assembly: is "jump if not zero" more expressive than "jump if odd"?

[mbaz]

I’m completely in favor of disallowing truthy and falsey values, and I hope the core team is never swayed otherwise. Having said that, this claim caught my eye:

@StefanKarpinski

But we could just as easily have had je and jo (jump if even, jump if odd) as assembly instructions that jump based only on the last bit of a register.

I teach an introductory programming course, and one of the concepts I introduce first is the “paper computer”. This is a computer that only exists on paper and runs by the user keeping track of its state using a pencil. My version has 16 words of code memory, 7 general purpose registers (R0 to R6), a program counter (PC) and five instructions:

• STP: stops execution
• SKP R#: R# == 0 ? PC <- PC+2 : PC <- PC+1
• JMP ##: PC <- ##
• ADD R#: R# <- R#+1, PC <- PC+1
• SUB R#: R# <- R#-1, PC <- PC+1

This instruction set is Turing complete, so it allows me to define “computational thinking” as “make this machine solve your problem for you”. Anyway, the first exercise is to write a program to add R0 to R1 and store the result in R2.

I’m wondering, can this problem be solved if the meaning of SKP R# is changed to “skip if even”? After a few minutes of thought, I’m leaning towards “no”, but I’d like to be proven wrong. If it can’t be done, it’d mean that there’s something fundamental in jz and jnz that is not shared by je and jo.