Question

An 8-bit weighted resistor digital-to-analog converter (DAC) has the smallest resistance of 500$\Omega$. The largest resistance has a value ___ k$\Omega$.

Answer 1

In general, in a binary weighted resistor DAC, the relationship between LSB and MSB resistance is given as :
LSB Resistance $=\left(2^{n-1}\right)$ MSB resistance where, n is the number of bits in the DAC.
Given, $n=8$
smallest resistance $=500\Omega$
MSB resistance $=500\Omega$
$\therefore \text{LSB resistance}=\left(2^{8-1}\right)\times 500\Omega$
$=128\times 500\Omega$
$=64000\Omega =64k\Omega$