These problems will solidify your understanding of manipulating boolean equations.
Full Adder Carry
Convert the carry logic for a full adder to use all NAND gates. Remember, an Inverter is just a 1 input NAND gate (or an N-input NAND gate with its legs tied together).
Full Adder Sum
We already covered the full adder on day 1 and found that the 'sum' output is equal to 'A xor B xor C'. Use the identity 'X xor Y = ~X&Y + X&~Y' and DeMorgan's law to expand this to a sum of products notation.
Be careful! On the second expansion of the XOR identity it is very easy to get the parenthesis wrong.
Check your resulting equation's truth table against the original truth table to verify.
Seven Segment Display
If you are still hankering for MOAR PROBLEMS, try implementing a seven segment display decoder. These displays are how a clock might display a number.
Do one segment at a time until you feel comfortable with K-Maps and Boolean Laws.
The link provided gives a truth table that can show the full hexadecimal range (0-F). You may choose to limit your self to decimal numbers only (whose clock tells time in hex?!). For the values that you no longer care about, put a 'x' in the corresponding cell on the Karnaugh Map. When drawing boxes, you can choose whether or not to cover these 'x's as is convenient.
... how do you handle those X's when doing a Boolean Law Reduction?
MOAR?!
You zealot you. Really, I'm flattered.
If you come up with other cool practice problems, please put them here.