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1 Lecture 4 Logic gates and truth tables Implementing logic functions Canonical forms Sum-of-products Product-of-sums 2 Logic gates and truth tables AND X•Y XY OR X + Y ... Example: Binary full adder 1-bit binary adder Inputs: A, B, Carry-in Outputs: Sum, Carry-out A B Cin Cout Sum Adder
Mapping truth tables to logic gates! Given a truth table " Write the Boolean expression " Minimize the Boolean expression " Draw as gates A B C F 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 F = A™BC™+A™BC+AB™C+ABC = A™B(C™+C)+AC(B™+B) = A™B+AC C A A’ B F 25 AND2 26 AND2 24 OR2
Problem: built by interconnecting building-block cells that implement simple functions, like basic logic gates. A commonly used type of standard cell are the and-or-invert (AOI) cells, which can be efficiently built as CMOS complex gates. Consider the AOI cell shown in Figure 3.70. This cell implements.
The basic logic gates are the inverter (or NOT gate), the AND gate, the OR gate and the exclusive-OR gate (XOR). If you put an inverter in front of the AND gate, you get the NAND gate etc. One of the common tool in specifying a gate function is the truth table.
Programming in C is a simplification of the C++ programming. Program Starting Point of ALL C PROGRAMS: Printing Usingprintf() (and include<stdio.h>): 03/printf.c. printf has a variable. int main() { number of arguments: int i = 42; First argument. char *s = "Hello, world!"; float f = 3.14;
Logic Gates • digital circuit that either allows a signal to pass through it or not. • Used to build logic functions • There are seven basic logic gates: AND, OR, NOT, NAND (not AND), NOR (not OR), XOR, and XNOR (not XOR) [later] Building Functions: Logic Gates A B Out 0 0 0 0 1 1 1 0 1 1 1 1 A B Out 0 0 0 0 1 0 1 0 0
The Duality Principle. “A Boolean expression that is always true is still true if we exchange OR with AND and 0 with 1” Proving the Theorems. Example: Theorem 1: x + x = x; xx = x. Proof: x + x. = (x + x) 1. postulate 2(b) = (x + x)(x + x’) 5(a) = x + xx’. 4(b) = x + 0. 5(b)
