====== Digital to analog converter ======
{{dac.png?400}}

Determine the output V<sub>out</sub> as a function of V<sub>0,1,2,3</sub>. What function does it perform? Build the circuit and verify its function by connecting V<sub>0,1,2,3</sub> to a dc voltage, one at a time. 

{{counter.png?200}}

Use a 4 bit binary counter({{datasheets/74163.pdf|74163}}) or an up/down counter({{datasheets/74F169.pdf|74169}}) outputs to drive V<sub>0,1,2,3</sub> in the circuit above. What waveform will you get? Build and verify. (To use 74169 as a synchronous counter: PE'=1, CEP'=0, CET'=0; P<sub>0-3</sub>=0; CP: clock input; Outputs at Q<sub>0-3</sub>; U/D'=1 for counting upwards and 0 for counting downwards). 

{{wave.png?400}}

Design a circuit to give the waveform above. You can use logic gates in addition to the counter.