divide and conqure algorithm

Q1)The algorithm for merging two sorted lists or arrays can be
modified to perform the union operation on two sets. Given
two sorted arrays A and B representing two sets of integers,
modify this algorithm so that it will produce as output the
union of the two sets.

Given a non-signed decimal integer M, we would like to convert it
into binary. For example, the decimal number “13” is equivalent to
the binary number 1101. Generating the digits of the binary number
can be done by a repeated division of the form:
M = q * 2 + r
where the remainder “r” is the next bit in the binary number and M
will be replaced by q before repeating this division operation to
generate the next new digit. For example, to generate the bits for
the decimal number 13, we perform:
13 = 6 * 2 + 1
6 = 3 * 2 + 0
3 = 1 * 2 + 1
1 = 0 * 2 + 1

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Design an algorithm by induction to generate (and print) the binary
digits of a given non-signed decimal number M.

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