| An alternative to the binary-weighted-input DAC 
    is the so-called R/2R DAC, which uses fewer unique resistor values. A 
    disadvantage of the former DAC design was its requirement of several 
    different precise input resistor values: one unique value per binary input 
    bit. Manufacture may be simplified if there are fewer different resistor 
    values to purchase, stock, and sort prior to assembly.
    Of course, we could take our last DAC circuit and modify it to use a 
    single input resistance value, by connecting multiple resistors together in 
    series:  
      Unfortunately, this approach merely substitutes one type of complexity 
    for another: volume of components over diversity of component values. There 
    is, however, a more efficient design methodology.  By constructing a different kind of resistor network on the input of our 
    summing circuit, we can achieve the same kind of binary weighting with only 
    two kinds of resistor values, and with only a modest increase in resistor 
    count. This "ladder" network looks like this:  
      Mathematically analyzing this ladder network is a bit more complex than 
    for the previous circuit, where each input resistor provided an 
    easily-calculated gain for that bit. For those who are interested in 
    pursuing the intricacies of this circuit further, you may opt to use 
    Thevenin's theorem for each binary input (remember to consider the effects 
    of the virtual ground), and/or use a simulation program like SPICE to 
    determine circuit response. Either way, you should obtain the following 
    table of figures:    
      
    
      
        | Binary  | Output voltage |  
        | 000  | 0.00 V |  
        | 001  | -1.25 V   |  
        | 010  | -2.50 V  |  
        | 011   | -3.75 V |  
        | 100 | -5.00 V  |  
        | 101  | -6.25 V  |  
        | 110  | -7.50 V  |  
        | 111  | -8.75 V  |    As was the case with the binary-weighted DAC design, we can modify the 
    value of the feedback resistor to obtain any "span" desired. For example, if 
    we're using +5 volts for a "high" voltage level and 0 volts for a "low" 
    voltage level, we can obtain an analog output directly corresponding to the 
    binary input (011 = -3 volts, 101 = -5 volts, 111 = -7 volts, etc.) by using 
    a feedback resistance with a value of 1.6R instead of 2R.  |