Reference

• Chapter 2 from An Animated Introduction to Digital Logic Design, 2nd Edition by John Carpinelli

Arithmetic table activity

In pairs/trios with dice.

1. Make a table with 2 input columns A and B and 5 empty columns (for a total of 7 columns).

2. For input A, there should be two possible values: 0 and [dice roll to get a number between 1 and 6]

3. For input B, there should be two possible values: 1 and [dice roll to get a number between 2 and 6 -- reroll on 1]

4. Repeat the following 6 times:

   1. Operator roll: roll a die to determine which arithmetic operator will be applied

      • 1 or 2: plus (+)

      • 3 or 4: times (*)

      • 5 or 6: negation (-)

   2. Input selection: roll a die to determine which input column(s) the operator is being applied to

      • remember that + and * are binary operators (require 2 inputs) and - is unary (requires 1 input)

      • if you roll a number that is for a column not yet populated, roll again

   3. Fill out column: apply the operator to the input column(s) and fill out the next column with the resulting values

5. Draw the corresponding arithmetic "circuit" for your table. You should have 2 input "toggles" and 5 operator "gates."

Boolean Logic table activity

In pairs/trios with dice.

1. Make a table with 2 input columns A and B and 5 empty columns (for a total of 7 columns).

2. For input A, there should be two possible values: 0 and 1

3. For input B, there should be two possible values: 0 and 1

4. Repeat the following 6 times:

   1. Operator roll: roll a die to determine which boolean operator will be applied

      • 1 or 2: or (∨)

      • 3 or 4: and (∧)

      • 5 or 6: not (¬)

   2. Input selection: roll a die to determine which input column(s) the operator is being applied to

      • remember that + and * are binary operators (require 2 inputs) and - is unary (requires 1 input)

      • if you roll a number that is for a column not yet populated, roll again

   3. Fill out column: apply the operator to the input column(s) and fill out the next column with the resulting values

5. Draw the corresponding arithmetic "circuit" for your table. You should have 2 input "toggles" and 5 operator "gates."

Abstraction activity

In pairs/trios, can you use only NOR (↓) to compute NOT, OR, AND and XOR?

• You might use a circuit diagram (https://logic.ly/demo/) to design your solution and check it with a truth table.

How can we add two binary numbers using boolean logic?

1. By Wed 9/23 end of day (11:59pm): complete Homework 2: Computing with Boolean Logic and submit via Gradescope