Digital Logic 1

The Basic Logic Design

       1.      Introduction

a.      Basic for digital computer.

b.      Fundamental for circuit and hardware communicate within computer.

c.       Represent of signals and sequences of a digital circuit through numbers 0(FALSE) and 1(TRUE).

d.      Mostly embedded in electronic devices such as calculators and computers.

Written by Soo Pheng Kian (B031210015)

      2.     Gates

-The fundamental building block of all digital logic circuit is the gate. Logical functions are implemented by the interconnection of gates.

      

-A gate is an electronic circuit that produces an output signal that is simple Boolean operation on its input signals. The basic gates used in digital logic are AND, OR, NOT, NAND, and NOR.

      

-Each gate has one or two inputs and one output. When the values at the input are changed, the correct output signal appears almost instantaneously, delayed only by the propagation time of signals through the gate (known as the gate delay).

     

-Typically, not all gate types are used in implementation. Design and fabrication are simpler if only one or two types of gates are used. Thus, it is important to identify functionally complete sets of gates. This means that any Boolean functionally can be implemented using only the gates in the set.

This is the Basic Logic Gates

Name	Graphic Symbol	Algebraic Function	Truth Table
AND		F = A •B or F = AB	A B F 0 0 0 0 1 0 1 0 0 1 1 1
OR		F = A + B	A B F 0 0 0 0 1 1 1 0 1 1 1 1
NOT		F = A̅ or F = A’	A F 0 1 1 0
NAND		F = (A̅ ̅B̅)	A B F 0 0 1 0 1 1 1 0 1 1 1 0
NOR		F = ( A̅ ̅+̅ ̅B̅ )	A B F 0 0 1 0 1 0 1 0 0 1 1 0
XOR		F = A.B̅ + A̅.B	A B F 0 0 0.1 + 1.0 = 0 0 1 0.0 + 1.1 = 1 1 0 1.1 + 0.0 = 1 1 1 1.0 + 0.1 = 0

Written by Low Foo Hwa (B031210343)

3.      Boolean Algebra

a.      Boolean algebra is the combination of logical variables and operations. Thus, a variable may take on the value 1(TRUE) or 0(FALSE) .The Basic logical operations are AND, OR, and NOT, which symbolically represented by dot, plus sign, and bar;

A AND B = A • B

A OR B = A + B

NOT A = A̅

A	B	A AND B	A OR B	NOT A	NOT B
0	0	0	0	1	1
0	1	0	1	1	0
1	0	0	1	0	1
1	1	1	1	0	0

b.      Laws of Boolean Algebra

Laws	AND Form	OR Form
Identity Law	A • 1 = A	A + 0 = A
Zero and One Law	A • 0 = 0	A + 1 = 1
Inverse Law	A • A̅ = 0	A + A̅ = 1
Idempotent Law	A • A = A	A + A = A
Commutative Law	A • B = B • A	A + B = B + A
Associative Law	A •(B • C ) = (A • B) • C	A + (B + C) = (A + B) + C
Distributive Law	A + (B • C) = (A + B) • (A + C)	A •(B + C) = (A • B) + (A + C)
Absorption Law	A(A + B) = A	A + A • B = A
DeMorgan’s Law	(A̅ ̅•̅ ̅B̅) = A̅ + B̅	(A̅ ̅+̅ ̅B̅) = A̅ • B̅
Double Complement Law	X̅̅=X

-          Prove (A̅B̅) ≠ A̅ • B̅

*Prove by using truth table!!!

A̅B̅= A̅ + B̅                  A̅ • B̅

                                                                                   

A	B	F
0	0	1
0	1	0
1	0	0
1	1	0

A	B	F
0	0	1
0	1	1
1	0	0
1	1	0

                               

Truth table A̅B̅ ≠ A̅ • B̅

Therefore , A̅B̅ ≠ A̅ • B̅.

c.      Boolean Equation Forms

Boolean equation can be represented in two forms:

Sum-of-product (SOP) – Combination of input that produce 1(TRUE) output.

                                           Form product of all variables.

                                           Sum each product.

Product-of-sum (POS) – Combination of input that produce 0(FLASE) output.

                                            Form product of all variables.

                                            Product each sum.

d.      Simplification of Boolean Equation

-          Use Laws of Boolean algebra to simplify Boolean expression.

-          Use Karnaugh Map to simplify Boolean expression.

Written by Mohd. Safar (B031210227)