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Qualcomm Software Engineer Interview Question

I interviewed in Boulder, CO and was asked:
"what is the significance of '20 log x'?"
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Part of a Software Engineer Interview Review - one of 979 Qualcomm Interview Reviews

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This convention is in place due to the original definition of Decibel (dB) as a measure of a ratio between powers. If X, X0 are power measurements( X0 could be the input or reference power, X the output ), then the dB measurement was defined as
X_dB = 10log_10 (X/X0)
This way, if X is 10 times X0, we read X is 10dB greater than X0. On the usefulness of utilizing the log_10: it allows to express a very large range of ratios in a range of moderate size, allowing one to clearly visualize huge changes of some quantity.
Many contributions to Control Theory have come from the area of Electrical Engineering. Since in a circuit with constant resistance, the power developed is proportional to the square of the applied voltage, then if V and V0 are two voltages of interest (I/O) one finds that:
V_dB= 10log_10(V^2/V0^2) = 20log_10(V/V0)
which is the reason why Electrical engineers use the dB defined as 20log_10(V/V0), and so Control theorists do!
- Dominic On on Jun 4, 2013
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C code for converting decimal to binary:

    char buff[10];
        int i;

    printf("enter the number\n");
    scanf("\n%d", &i);
    itoa(i,buff,2);

        printf("%s", buff);
- Solx on Jul 13, 2013

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