21 February, 2000

The quiz

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

generate if both bits are 1
- g_i = x_i y_i
propagate if one bit is 1
- p_i = x_i + y_i
carry if
- c_i+1 = g_i + p_i c_i
What the book suggests...
- p_i = x_i XOR y_i
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
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