The propagation delays of the XOR gate, AND gate and multiplexer (MUX) in the circuit shown in the figure are $4 \mathrm{~ns}, 2 \mathrm{~ns}$ and 1 ns respectively.

If all the inputs $P, Q, R, S$ and $T$ are applied simultaneously and held constant, the maximum propagation delay of the circuit is

A digital transmission system uses a $(7,4)$ systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-code word pairs in this code ( $m_i ; c_i$ ). Where $c_i$ is the codeword corresponding to the $i^{\text {th }}$ message $m_i$, are known to be $(1100 ; 0101100),(1110 ; 001 1110)$ and $(0110 ; 1000110)$, then which of the following is a valid codeword in this code?

Addressing of a $32 K \times 16$ memory is realized using a single decoder. The minimum number of AND gates required for the decoder is :

An 8-bit unipolar (all analog output values are positive) digital-to-analog converter (DAC) has a full-scale voltage range from 0 V to 7.68 V . If the digital input code is 10010110 (the leftmost bit is MSB). Then the analog output voltage of the DAC (rounded off to one decimal place) is

$\_\_\_\_$ V.