Note: AB means (AB)

1. Please create the truth table logic equation, and gate diagram (OPTIONAL). If you have no access to software Logic Friday, you can do it by paper and pencil.

• for G = AB + (CD + EF)'
• a 4 to 1 MUX. Inputs to the mux are all 1 bit. How many input signals do you need? Dont forget the select line. You will need 2 select lines.

2. How would you design the hardware for a multiplier multiplying two signed integers (-8 to +7). How many bits is the output of the multiplier? Hint: The output (product) will range from -64 to +49

• How do you design the bit extension? How many bits do you need to extend?

3. Subtractor

One of the ways to implement a subtractor is to rearrange the equation this way.

• F = A B
• F = A + (-B)

You need the adder block to add 2 numbers (2s complement)

What extra block do you need? How would you connect this block to the adder block? How do you implement the function inside the parenthesis? What does the logic diagram look like? Please use a 4 bit number as an example.

3. The signals ld and rst could be 0 or 1.

If rst is 0, what is the output q as a function of din?

If rst is 1 and ld is 1, what is the output q as a function of din?

0 q_nxt[7:0] q[7:0] 8b reg din[7:0]] 8 Id rst clk 0 q_nxt[7:0] q[7:0] 8b reg din[7:0]] 8 Id rst clk