Can a computer execute a billion operations in seconds?
Yes. The IBM Sequoisa can perform 16,320 trillion floating point operations per second. That's 16.32 petaflops. A billion operations is nothing by comparison.
One cycle, in a computer, takes a time that is the reciprocal of the computer's clock rate - that which is expressed in MHz, or - more commonly nowadays - in GHz. Example: if your computer has a clock rate of 3 GHz, the time for a single cycle is (1 / 3 billion) seconds, i.e., 1/3 of a nanosecond, or 333 picoseconds.
Check your math and your answer....one billion divided by 31,536000 = 31.7 years, not 31 thousand years. It is actually 31 years, 259 days, 1 hour, 46 minutes and 40 seconds 1 Billion seconds equal 1 billion divided by the number of seconds in a year (31,536,000) equals 31,709.79 years. So just about 32 thousand years