## PHYS345 Electricity and Electronics

Hint for S9.3

Refer to your notes from our recent class and model after the proof of DeMorgan's first theorem that was presented.

This is the gate combination constructed directly from the Boolean expression.

Refer to your class notes on our discussion of segment a. Also, warm up on the Karnaugh map started for the simpler gate combination for segment c.

Construct a truth table with three inputs, A, F, and Bi and two outputs, D and Bo.

Think back to elementary subtraction facts:
A=1, F=1, Bi=0: With no borrow input, 1-1=0 and no borrow output. Right?
A=0, F=1, Bi=0: With no borrow input, 0-1=1 with the borrow output set.
A=1, F=0, Bi=1: With the borrow input set, 1-0-1=0 with no borrow output.
Determine the rest of the truth table entries.

Convert to two Karnaugh maps, one for each output. Follow the textbook's example for the full adder.

"http://www.physics.udel.edu/~watson/phys345/protected/exercises/hints/1029.html"
Last updated Oct. 30, 1998.
Copyright George Watson, Univ. of Delaware, 1998.