Given information:
- PCM system uses uniform quantizer followed by a 7-bit binary encoder
- Bit rate of the system is 50x10^6 bits/second
- Full-load sinusoidal modulating signal of frequency 1MHz is applied to the input

To find:
- Output signal to quantization noise ratio

Solution:
1. Bit rate of the system can be calculated using the formula:
Bit rate = (sampling rate) x (quantization bits per sample)
Here, since a 7-bit binary encoder is used, quantization bits per sample = 7.
Sampling rate can be calculated as follows:
- According to Nyquist-Shannon sampling theorem, the minimum sampling rate should be twice the maximum frequency component of the input signal.
- Here, the input signal is a full-load sinusoidal signal of frequency 1MHz. So, the maximum frequency component is 1MHz.
- Therefore, the minimum sampling rate required = 2 x 1MHz = 2MHz.
- However, since the system uses uniform quantizer, the sampling rate must be higher than the minimum required rate. A common practice is to use a sampling rate 4-5 times higher than the minimum required rate.
- Let's assume the sampling rate is 4 times the minimum required rate, i.e., 4 x 2MHz = 8MHz.
- Therefore, the bit rate = 8MHz x 7 = 56Mbps.

2. The input signal is a full-load sinusoidal signal, which means it uses the full range of the quantizer. In this case, the quantization noise can be assumed to be uniformly distributed between -Δ/2 and +Δ/2, where Δ is the quantization step size.
- The quantization step size can be calculated as follows:
Δ = (maximum input signal amplitude) / (number of quantization levels)
- Here, since a 7-bit binary encoder is used, number of quantization levels = 2^7 = 128.
- The maximum input signal amplitude can be assumed to be the full range of the quantizer, which is 2^7-1 = 127 (since 7 bits can represent numbers from 0 to 127).
- Therefore, Δ = 127 / 128 = 0.9922.

3. The output signal power can be calculated as follows:
- The input signal power can be assumed to be uniformly distributed between -A and +A, where A is the maximum amplitude of the input signal. Here, A = 127 (as mentioned earlier).
- The input signal power = (A^2) / 2 = 10112.5.
- The output signal power can be calculated by assuming that the quantization noise is uncorrelated with the input signal. In this case, the output signal power = (quantization step size)^2 / 12.
- Therefore, output signal power = (0.9922)^2 / 12 = 0.0082.

4. The output signal to quantization noise ratio can be calculated as follows:
- Output signal power / quantization noise power
- Quantization noise power = (Δ^2) / 12 = 0.0007.
- Therefore, output signal to quantization noise ratio = 0.0082 / 0.0007 = 11.71.
- Converting to decibels