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Notes on Architecture

Dave Rosoff

Section 3.1 Problems for Monday, Jan 8

Make sure you can solve all of these problems. Similar ones will appear on the midterm. As always in courses at this level, “solve” means to give complete supporting reasoning or justification, not just the answer. In this case you should include the details of your calculation, however you do it.

Exercises Exercises

1.

For each problem below, interpret the summands as binary-encoded integers and find the sum without converting the summands to decimal. Express all your answers in binary, and for each problem, show a complete record of your reasoning. This could be a collection of \(1 \to 2\) machines as in the videos we saw in class, a pencil-and-paper addition with carries, or anything else that shows me how you came up with your answer.
(a)
Add the following binary numbers: \(1011 + 1101\)
Answer.
11000.
(b)
Perform the binary addition: \(11100 + 1011\)
Answer.
100111.
(c)
Add the binary numbers: \(10010 + 1101\)
Answer.
11111.
(d)
Compute the sum: \(1111 + 101\)
(e)
Perform binary addition: \(101010 + 11011\)
(f)
Add the binary values: \(1111 + 111\)
(g)
Compute the sum of: \(10101 + 110\)
(h)
Add the binary numbers: \(110110 + 1011\)
(i)
Perform binary addition: \(1111 + 1001\)
(j)
Add the binary values: \(101010 + 110\)

2.

For each problem below, interpret the summands as hexadecimal-encoded integers and find the sum without converting the summands to decimal. (You are allowed to convert them to binary, but I don’t necessarily recommend it.) Express all your answers in hex, and for each problem, show a complete record of your reasoning. This could be a collection of \(1 \to 2\) or \(1 \to 16\) machines as in the videos we saw in class, a pencil-and-paper addition with carries, or anything else that shows me how you came up with your answer.
(a)
Add the hexadecimal values: \(C_{16} + 7_{16}\)
Answer.
\(13_{16}\)
(b)
Perform the sum: \(F2_{16} + 4_{16}\)
Answer.
\(F6_{16}\)
(c)
Compute the sum: \(1D_{16} + A_{16}\)
Answer.
\(27_{16}\)
(d)
Perform the sum: \(1F_{16} + A_{16}\)
(e)
Add the hexadecimal numbers: \(1A_{16} + 2F_{16}\)
Answer.
\(49_{16}\)
(f)
Compute the sum: \(3B_{16} + 4D_{16}\)
(g)
Add the hexadecimal values: \(A1_{16} + B2_{16}\)
Answer.
\(153_{16}\)
(h)
Add the hexadecimal numbers: \(2C_{16} + 13_{16}\)
(i)
Compute the sum: \(1AB_{16} + 2F_{16}\)
(j)
Add the hexadecimal numbers: \(3E_{16} + 25_{16}\)
(k)
Add the hexadecimal numbers: \(A7 + F9\)
(l)
Add the hexadecimal numbers: \(C5 + 13B\)
(m)
Add the hexadecimal numbers: \(124 + 17C\)
(n)
Add the hexadecimal numbers: \(1F3 + 1A7\)
(o)
Add the hexadecimal numbers: \(266 + 1C2\)
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