- Wednesday, 1 March
- Covers roughly Chapter 1 to Section 4.3 (don't cares)
- Closed book
- List of algebraic indentities will be provided
- Fill-in-the blank truth tables will be provided
- Fill-in-the blank Karnaugh maps will be provided

- Sources of problems
*Homework assignments*- Lab

- Full adder
- s
_{i}= x_{i}XOR y_{i}XOR c_{i} - c
_{i+1}= x_{i}y_{i}+ c_{i}(x_{i}XOR y_{i}) - c
_{i+1}= x_{i}y_{i}+ c_{i}x_{i}+ c_{i}y_{i}

- s
- ripple-carry adder
- Composed to full adders
- Has significant propagation delay

*generate*if both bits are 1- g
_{i}= x_{i}y_{i}

- g
*propagate*if one bit is 1- p
_{i}= x_{i}+ y_{i}

- p
*carry*if- c
_{i+1}= g_{i}+ p_{i}c_{i}

- c
- What the book suggests...
- p
_{i}= x_{i}XOR y_{i}

- p
- Continuing the job
- c
_{i+1}= g_{i}+ p_{i}c_{i} - c
_{i+2}= g_{i+1}+ p_{i+1}g_{i}+ p_{i+1}p_{i}c_{i} - c
_{i+3}= g_{i+2}+ p_{i+2}g_{i+1}+ p_{i+2}p_{i+1}g_{i}+ p_{i+2}p_{i+1}p_{i}c_{i} - c
_{i+4}= g_{i+3}+ p_{i+3}g_{i+2}+ p_{i+3}p_{i+2}g_{i+1}+ p_{i+3}p_{i+2}p_{i+1}g_{i}+ p_{i+3}p_{i+2}p_{i+1}p_{i}c_{i}

- c
- and yet more
- c
_{i+4}= g_{(i,i+3)}+ p_{(i,i+3)}c_{i} - g
_{(i,i+3)}= g_{i+3}+ p_{i+3}g_{i+2}+ p_{i+3}p_{i+2}g_{i+1}+ p_{i+3}p_{i+2}p_{i+1}g_{i} - p
_{(i,i+3)}= p_{i+3}p_{i+2}p_{i+1}p_{i}

- c

Or using the on-line notes of Shivkumar Kalyanarama of the Rensselaer Polytechnic Institute