The universal gas constant, denoted by R, can be calculated using the Avogadro number (N_A) and the Boltzmann constant (k_B) by the following relationship:

$$ R = N_A \times k_B $$

Given that:

$$ N_A = 6.023 \times 10^{23} \text{ mol}^{-1} $$ $$ k_B = 1.380 \times 10^{-23} \text{ J K}^{-1} $$

Let's multiply these values to find R:

$$ R = (6.023 \times 10^{23} \text{ mol}^{-1}) \times (1.380 \times 10^{-23} \text{ J K}^{-1}) $$ $$ R = (6.023 \times 1.380) \times (10^{23} \times 10^{-23}) \text{ J mol}^{-1} \text{K}^{-1} $$ $$ R = 8.31174 \times 10^{0} \text{ J mol}^{-1} \text{K}^{-1} $$

To determine the number of significant digits in the calculated value of R, we must consider the number of significant digits in the given values of N_A and k_B.

The value for N_A has four significant digits (6.023), and the value for k_B also has four significant digits (1.380). When multiplying or dividing numbers, the number of significant digits in the result is determined by the number with the smallest amount of significant digits used in the calculation.

In this case, since both constants have four significant digits, the value of R calculated from their multiplication will also contain four significant digits:

$$ R \approx 8.314 \text{ J mol}^{-1} \text{K}^{-1} $$

Therefore, the calculated value of the universal gas constant R has four significant digits.