Voltage offset Op Amp

Hello. I'm planning on designing a MIDI to CV converter. Didn't start the design yet, i'm thinking about the possibilities.
For the output i'll use an R2R ladder 8bit DAC. Then after that there's an op amp with a buffer stage, and then a non inverting amplifier. I use the amplifier to change the scale of the voltage output to 1v/oct ( steps of 0,0833v). For example, I have a digital value of 12, and the voltage output would be 0,235v then I have to multiply that by 4,25 to make it 1v. Then, this happens every 12 values, when it's 24, the output is 0,470v, and after the op amp would be 2v and so on. One of the resistor of the amplifier will be a trimpot for fine calibration.
But the problem is the op amp offset. I suppose I will use a cheap and common one, like lm358.
When digital is 0, the ouput is 0v. And as I understand, if the op amp has 0v at the input it won't do anything, or won't work as expected because it's under the offset voltage input, which on the lm358 is 2.9mv - 7mv .
How can I "fix" this? I need to have the 0v enter the op amp, and ouput 0v.
thanks

Simple - provide a negative voltage. The LM358 isn’t rail to rail input or output. In fact, no Op Amp really is true rail to rail, only close to it.

It is much simpler to just provide that negative voltage to the Op Amp. It doesn’t take much. Toggle one of the outputs from the Arduino (using PWM set to 127 or 50% will work) through a capacitor/diode inverter.

Use shottky diodes. Like this:

  1. use a precision rail-to-rail opamp.
  2. use an opamp with trim inputs
  3. http://e2e.ti.com/blogs_/archives/b/thesignal/archive/2012/08/27/where-are-the-trim-pins.aspx?DCMP=HPA-PA-AMP-OPA192&HQS=hpa-pa-amps-opa192-thehub-20140122-lasertrim-blog-en
It is much simpler to just provide that negative voltage to the Op Amp. It doesn't take much. Toggle one of the outputs from the Arduino (using PWM set to 127 or 50% will work) through a capacitor/diode inverter.

I put the negative voltage from the arduino to the negative input of the opamp?(with related resistors) But that will vary the gain right? It should have a gain of 4,25
So, it's as simple as that? Thanks

The gain of the Op Amp will not vary if the negative voltage changes. You do want to make sure the smoothing capacitor on it is enough to smooth out the pulses from the Arduino, and I'd also add a 0.1uF ceramic capacitor to bypass any high frequency noise.

Keep in mind that the LM358 output can only go as high as Vcc - 1.5V. Same with the common mode input voltage. There are newer Op Amps with better specs.

polymorph:
The gain of the Op Amp will not vary if the negative voltage changes. You do want to make sure the smoothing capacitor on it is enough to smooth out the pulses from the Arduino, and I'd also add a 0.1uF ceramic capacitor to bypass any high frequency noise.

Keep in mind that the LM358 output can only go as high as Vcc - 1.5V. Same with the common mode input voltage. There are newer Op Amps with better specs.

Right, thanks.
I'll power it with 12V, and i only need 0-5v range, so I suppose i'm fine.
I've seen many circuits that instead of using an non inverting amplifier uses two inverting in series. Which way should I do it?
thanks