hiiii,
i am just wondering, like in missiles, lets say speed is Mach 2, and if its a intercept missile, its needs to act very fast right when it get close to the other missile, so i am wondering what kind of clock speed they used. and what kind of embedded systems they used? and other technical details. recourses links and etc,
thank youuu 
For any answer, you need to supply other technical details. like how your missile KNOWS it is getting close. Most intercept missiles use an exploding charge to disable the other missile. A near miss is very effective!
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You'll not find out - the information is classified.
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Now I am wondering if is possible to build a missle like that that only uses hardware…..
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Guided missiles certainly pre-date computers small enough to drive them.
At mach 2 something is travelling on the order of 700m/s. That's 700mm/ms. That's 700um/us.
A microsecond is a pretty long time even for our slow AVR micros. If you've got processors running in the GHz range then you're talking about having thousands of clocks per micron of movement.
I don't know what it takes and I certainly wouldn't attempt to conjecture publicly, but I'm betting that GHz speeds are more than enough.
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in Iron Dome Missille defence system they used detecting system called "electro optical targeting system" (i dont know what that mean, thats what they said in the video 
)
Doesn't have to be digital:
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They are dealing with ballistic missiles. So they know the trajectory the missile will take as soon as it reaches it's maximum speed. They track it visually using X and Y coordinates and that gives them the the future location of the missile up to the point of impact. The coordinates for the defensive missile are programed to cross the coordinates of the incoming missile. When close enough, the defensive goes bang!
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woow....thank you for the answers
what should i do if wanna learn more, in-depth about this topic? i am open to suggestions 
Here are some US Navy documents on missiles and Fire Control Systems from decades ago. As @dougp said, they don't have to be digital.
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awww... thank youu
much appreciated
Take and pass all the math and science classes you have access to!
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It's really interesting stuff. I don't know if it's on that list, but they have some documents published from the early 1900's (like around 1920) on the math for fire control systems for battleship guns. Amazing to think how sophisticated they were 100 years ago.
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Become an engineer for a missile company or the military………
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