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.

The propagation delay of the exclusive-OR (XOR) gate in the circuit in the figure is 3 ns . The propagation delay of all the flip-flops is assumed to be Zero. The clock (Clk) frequency provided to the circuit is 500 MHz .

Starting from the initial value of the flip-flop outputs $Q_2 Q_1 Q_0=111$ with $D_2=1$, the minimum number of triggering clock edges after which the flip-flop outputs $Q_2 Q_1 Q_0$ becomes 100 (in integer) is $\_\_\_\_$