Ask HN: Should a CEO be able to code?

I've worked in places where the CEO is basically the technical co-founder and also in places where the CEO barely had a fleeting grasp of common HTML tags (both were web-oriented companies, both were small startups). The biggest guys like Google, Facebook, etc. seem to put people with CS/engineering backgrounds at the helm... I've even read that Zuckerberg occasionally commits some production code himself.

Obviously that's far from the core responsibilities of a CEO. My question is oriented towards whether a CEO being able to grasp the technical concepts on a deeper level actually makes a difference to the success of the company.

Interestingly enough, the company I worked for with the non-technical CEO actually made a lot more money and is AFAIK much more successful than the other I mentioned. I'm just curious about other peoples' experiences with this.