calculating clock speed with cycle time?

"then I do 1/0.000000266"

yes.

= 37593989.496Hz"

Not quite. You've moved the decimal a bit. Sometimes this is easier in scientific notation:

1/0.000000266

1 / 2.66x10^-7s

(10^7) * (1/2.66s)

(10^7) * 0.37593

3.76 x 10^6 (or 3760000). You were off by a factor of 10.

"to make it Mhz i do 37593989.496Hz x 10^6?"

No, other way around.

If you have 1000000 joules, you have 1 megajoule.

If you have 3760000Hz, you have 3.76 MHz.

T = 266 ns = 266E-9 seconds, where "nano" means 1E-9. Use the scientific notation for these tiny values, you'll find it easy to do.

And as frequency F = 1/T, we have F = 1/266E-9 = 0.003759398E9 = 3759398 cycles/second or 3.76E6 Hz ANS.

Here's a rule that should stand you in good stead for all types of these problems. You have a basic mathematical relation there:

(Clock speed) = 1 / (cycle time)

ƒ = 1/τ

You're given one of the quantities, and you want to get the other. So just treat all your units like algebraic constants, and all the usual rules of algebra apply -- you can:

• Replace equals with equals

• Multiply by 1 = ratio of any two equals

• Multiply or divide both sides of an equation by equals

And use the definition:

Hz = 1/s

Multiply both sides by 10⁶:

MHz = 10⁶/s = 1/(10ˉ⁶s) = 1/µs

So then,

τ = 266 ns = 0.266 µs

ƒ = 1/τ = 1/(0.266 µs) = (1/0.266) MHz = 3.76 MHz