Fan-out

Fan-out is the number of loads that the output of a gate can drive without decreasing the performance of the logic gate.
Fan-out depends on the logic family of related gate.

Fan-in

Fan-in is the number of inputs available on a logic gate.



Fan in is 2 in the and gate diagram above.
There are 2 inputs on this gate.

Boolean Algebra

Basic identities used in boolean algebra digital logic.

Note that X' means not X, the complement of X

1. X+0 = X
2. X.1 = X
3. X+1= 1
4. X.0 = X
5. X+X = X
6. X.X=X
7. X+X'=1
8. X.X'=0
9. X''=X

Other boolean algebra properties.

• Commutative: X+Y = Y+X
• Associative: X+(Y+Z) = (X+Y)+Z
• Distributive: X(Y+Z) = XY + XZ
• DeMorgan's: (X+Y)' = X'+Y'

The identities below are useful for simpling the logic equations.

• X(X+Y)=X
• (X+Y)(X+Y')=X
• X(X'+Y)=XY

Boolean algebra digital logic tutorial.

BCD Binary Decimal Codes

Binary decimal codes contains 0 to 9 numbers, that is human readable, unlike computer systems use binary number systems 0 and 1s.

Decimal Number	BCD Digit
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001

BCD example

(215)₁₀ = (0010 0001 0101)_BCD



BCD Binary Decimal Codes tutorial

Octal Number System

Octal number system is base-8 system with 8 digits 0 to 7.

Example of a octal number: 147.2

Expanding numbers as a power series with base of 8.

Example of octal number:

(147.2)₈ = 1x8<sup>2 + 4x81 + 7x80 + 2x8-1 = 64 + 32 + 7 + 0.25 = (103.25)₁₀


Octal number system tutorial.</sup>

Binary Number System

Binary number system is base-2 system with 2 digits 0 and 1.

Example of a binary number: 1101.1

Binary number can be expanding numbers as a power series with base of 2.

Example:

(1101.1)₂ = 1x2³ + 1x² + 0x2¹0 + 1x2^-1 = (13.5)₁₀

Binary number 1101.1 is equal to 13.5 in base-10 number system.

Also 1K (kilo) = 2¹⁰
Also 1M (mega) = 2²⁰


Binary number system tutorial