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Notes on Architecture

Dave Rosoff

Section 1.1 Binary and Exploding Dots

Watch the video below before doing Activity 1.1.1.

Activity 1.1.1.

What is the \(1 \to 2\) machine’s code for 23?
  1. 11101
  2. 10111
  3. 11011
  4. 11111

Activity 1.1.2.

How many is a single dot in the \(k\)th box from the right worth?
  1. \(\displaystyle 2(k - 1)\)
  2. \(\displaystyle 2k\)
  3. \(\displaystyle 2^{k-1}\)
  4. \(\displaystyle 2^k\)

Activity 1.1.3.

What number does the \(1 \to 2\) code \(1001~0110\) represent?
  1. 142
  2. 144
  3. 150
  4. 158

Activity 1.1.4.

What is the biggest number a \(1 \to 2\) machine with four slots can represent? Eight slots?
Watch the video below before doing Activity 1.1.5.
Watch the video below before doing Activity 1.1.6.

Activity 1.1.7.

To perform addition using a \(1 \to 2\) machine, simply put the codes into a machine together, then perform the explosions.

(a)

Show how you add \(4 + 6 = 10\) in a \(1 \to 2\) machine.

(b)

Show how you add \(19 + 17 = 36\) in a \(1 \to 2\) machine.

(c)

Now let’s switch to the \(1 \to 10\) machine. Use one to add \(385 + 719 = 1104\text{.}\) Then perform the addition the traditional way. What do you notice? Designate a reporter to give your idea to the big group.
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