How Can I Achieve a Precise One-Second Pulse for My Timer Project?

[Feenix]

Homework Statement

It's simple, I need a simple timer, that when powered on, will count down from a variable amount of seconds that are preferably shown on several 7 segmant displays, when the timer hits "0" the output goes high, simple as.
I figured I'd build it in 2 stages, the 555 timer to pulse every 1 second, then a counter of some sort (still yet to research that bit in depth) to store the timer pulses...

The help I need is this: I can't figure out the right values to get the 555 to pulse EVERY 1 second so make a perfect countdown timer. I tried using R1: 1K ohms R2: 7K ohms and C1: 100 nano farads. Gives me a time of "1.0394999999999999 seconds" which is close yes... but not close enough, and I know that resistors have discrepancies and what not, but I want it to be as close as possible, also. I remember something from college about the E32 series going up evenly... So is this the closest I can get?
Is there a chip that is set to exactly 1 second? Like a clock chip?

I also need a lot of help on a counter. Anyone know of a good link where I can look them up?

Please note this is for a home project.

Homework Equations

T = 0.7 X (R1 + 2R2) X C1

The Attempt at a Solution

This is my circuit diagram, drawn in MS Paint :D

 

[vk6kro]

555s are not really meant for use as high precision clocks, but you could get closer with a 10K multi-turn pot instead of your 7K resistor.

But you would need a much larger capacitor.
Don't forget the capacitance in that formula is in Farads.

I checked the frequency of your oscillator and it seems it should be oscillating at 960 Hz.
http://freespace.virgin.net/matt.waite/resource/handy/pinouts/555/index.htm

A better way would be to divide down from a crystal oscillator.

For example you could start with a 100 KHz crystal and divide by 10 to get 10 KHz then again to get 1 KHz with a 4518 chip then by 1000 with a 4059 chip to get exactly 1 Hz.
Or, because the 4059 chip is tricky, you could just use more 4518 chips to get to 1 Hz.

These 4518 chips are two divide-by-10 devices in one package so you can divide by 100 easily.

If this isn't homework you can post stuff like this on the Electrical Engineering section.

 

[vk6kro]

Great drawing. Pin 5 normally has a capacitor to ground, though.

I find it hard to locate the text properly with the text tool.
So, I write it somewhere that doesn't matter then turn off "opaque" (from Image pulldown) then use the selection tool (dotted rectangle) to move the text to where I want it.

There is a control G function that gives you a grid when on magnify mode. Useful.

You can make the erase device smaller or larger with control minus or control +
Handy to show that crossing wires do not touch. Just draw them crossing and erase a small line above and below the horizontal wire.

If you want to draw blobs to show connection, use the filled circle. Start northwest of the centre point by the radius of the circle. The arms of the crosshairs are a good guide for this.
Hold the mouse button and draw towards the southeast by the same amount. Should get a perfect circle.