Relevant portion of assembly (no optimizations):
cmpl $1, -20(%rbp)
movzbl %al, %eax
orl %eax, -4(%rbp)
Most other architectures have one of:
1) condition codes that you can use to predicate an "or $r1, $r1, 1" (e.g., ARM)
2) compare instructions that put a 1 or a 0 in a result register, which can be directly ORed in. (e.g., MIPS)
Of course, that code only works if you are either not writing in C89 or if your compiler and ISA conspire to always return exactly one from true boolean expressions. It is my understanding that the C89 standard only requires "nonzero," so you might need "a |= (b != c) ? 1 : 0;*" instead.
YMMV depending on compiler and architecture, but the 2 or 3 platforms I tried without passing any opti flags were branchless.