1.1. Digital Computers
program is a sequence of instructions that a computer reads and follows in order to carry out some task.
central processing units, or CPUs, electronic memory (RAM and ROM) , and several input-output (I/O) devices.
1.2. Logic GatesKnow truth table, Boolean algebraic symbol, and circuit symbol.
1.3. Boolean AlgebraThree ways to represent Boolean Functions:
x1'*x2'*x3'*x4' = (x1 + x2 + x3 + x4)'
x1' + x2' + x3' + x4' = (x1*x2*x3*x4)'
Dual Symbols for NOR and NAND resulting from DeMorgan's theorem.
Truth table: Interchange 0's and 1's under the F column.
Boolean expression: Add a ' around the whole expression. Simplification derived from DeMorgan's theorem.
F = AB + C'D' + B'D F = (AB + C'D' + B'D)' = (A' + B')(C + D)(B + D')
1.4. Map Simplification
- Draw map.
- Box largest possible adjacent squares with 1's.
- Determine what properties squares within box have in common.
1.5. Combinational CircuitsA combinational circuit is one whose outputs at a given time depend only on the inputs a short time prior. If a combinational circuit has inputs x, y, and z, and outputs a and b, then:
a = f(x,y,z)and
b = f(x,y,z)Time is only a factor because of propagation delays in the circuit. I.e., the output a will not change instantaneously when input x changes, but will change after the new signal x propagates through the gates and wires that connect x to a.
Adds two bits (augend and addend) to produce a 1-bit sum and a 1-bit carry.