Lecture 10 Ticket

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1. Multiply the binary numbers 1011010 and 110111 by hand using the algorithm described in the Binary Representation notes. Check your work by converting the numbers to decimal and performing the decimal multiplication as well. Please show your work.

2. Suppose \(a\) and \(b\) are both represented with \(n\) bits. What is the running time of \(\mathrm{Multiply}(a, b)\) as a function of \(n\)? (Be sure to account for the running time of the call to \(\mathrm{Add}\).) If \(a\) and \(b\) satisfy \(a, b \leq N\), what is the running time of \(\mathrm{Multiply}(a, b)\) as a function of \(N\)?