A shift register can operate in four modes: Serial In – Serial Out, Serial In – Parallel Out, Parallel In – Serial Out, and Parallel In – Parallel Out (PIPO). The PIPO mode allows for parallel input and output.

Solution:

To find the next state, a K-map can be created with the control and current state serving as the axes. The resulting map can be used to derive the next state, as shown in the table below. The blue and red groupings represent the possible next states for a and b, respectively.

$$

begin{array}{lc|cccc}

&& rlap{AB_text{(current state)}} \

& & 00 & 01 & 11 & 10 \hline

XY & 00 & color{blue}{1}color{red}{1} & color{blue}{0}color{red}{0} & color{blue}{1}color{red}{0} & color{blue}{0}color{red}{1} \

& 01 & color{blue}{0}color{red}{1} & color{blue}{1}color{red}{0} & color{blue}{0}color{red}{0} & color{blue}{1}color{red}{1} \

& 11 & color{blue}{0}color{red}{1} & color{blue}{1}color{red}{1} & color{blue}{1}color{red}{0} & color{blue}{0}color{red}{0} \

& 10 & color{blue}{1}color{red}{0} & color{blue}{0}color{red}{0} & color{blue}{0}color{red}{1} & color{blue}{1}color{red}{1} \

end{array}

$$

Please note that the equations provided are deliberately incomplete and the accuracy of the k-map entries may vary. In case you find it difficult to identify the groups from a double variable, you can split them into separate k-maps – one for red entries and the other for blue entries.

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