Announcments

Homework 5 is due on Oct 15th, 9 AM before class.

Read 3.1 to 3.33 of textbook by Wednesday.
Half adder
Design a Multioutput circuit that adds two 1bit binary numbers \(x_0\) and \(y_0\) and outputs a sum \( s_0 \) and carry bit \( c_1 \).
\( x_0 \)  \( y_0 \)  \( s_0 \)  \( c_1 \) 
0  0  0  0 
0  1  1  0 
1  0  1  0 
1  1  0  1 
Half Adder
Full adder
Design a Multioutput circuit that adds three 1bit binary numbers \(x_i\), \(y_i\) and \(c_{i}\) outputs a sum \( s_i \) and carry bit \(c_{i+1} \).
\( c_i \)  \( x_i \)  \( y_i \)  \( s_i \)  \( c_{i+1} \) 
0  0  0  0  0 
0  0  1  1  0 
0  1  0  1  0 
0  1  1  0  1 
1  0  0  1  0 
1  0  1  0  1 
1  1  0  0  1 
1  1  1  1  1 
Full adder
Brown and Vranesic (2014)
Decomposed Full adder
Design a Full adder in terms of two Half Adders
Decomposed Full adder
Brown and Vranesic (2014)
Ripple carry adder
Design a 4bit adder using 4 Full adders
Ripple carry adder
Brown and Vranesic (2014)
More circuit symbols
Multiplexer
Adder
More circuit symbols
Multiplexer
Adder
Design a 4bit Adder/Substractor unit
Using an adder and 1's complement unit.
Adder/Substractor unit
Gray code