Digital Electronics - Tutorial 1: Number System - Introduction to Binary, Octal, Hexadecimal Systems with conversions to/from the Decimal System



Number System

 



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                                                                     Digital Electronics Tutorial 1: The Number System


Here's a quick look at the contents of this tutorial.


The general idea is to introduce you to the different number systems: Binary, Octal etc. and how to convert those numbers to/from the decimal number system.

How do you convert a binary to decimal?


Lets do this by considering an example--
--------------->Convert 11010 to decimal.
1) First write the binary number as-
1 1 0 1 0

2) now below every digit write the weight of that position as-
1 1 0 1 0
4 3 2 1 0
2 222 2

3) rewrite them in the expanded form as-
1 1 0 1 0
16 8 4 2 1

4) then multiply the corresponding values and add the resulting terms
1*16 + 1*8 + 0*4 + 1*2 + 0*1
= 16 + 8 + 0 + 2 + 0
= 26

How to convert a decimal number into binary form?


To convert a decimal number to binary, keep dividing the number by 2 until the quotient
reaches 0 and note all the remainders obtained after every division.
For example--
------------->Convert 73 to binary..
quotient
remainder
73/2 = 36
1
36/2 = 18
0
18/2 = 9
0
9/2 = 4
1
4/2 = 2
0
2/2 = 1
0
1/2 = 0
1

Note: write the remainders in reverse order i.e. from bottom to top. So the binary equivalent of 73 is 1001001.


Similarly, you will also learn about important conversions between octal, hexadecimal, binary and decimal numbers with examples.


Complete Tutorial with Solved Examples : (Part - I)



Here's a list of all the tutorials we currently have in this area - Introductory Digital Electronic Circuits and Boolean logic

 Introduction to the Number System : Part 1 
Introducing number systems. Representation of numbers in Decimal, Binary,Octal and Hexadecimal forms. Conversion from one form to the other.
 Number System : Part 2 
Binary addition, subtraction and multiplication. Booth's multiplication algorithm. Unsigned and signed numbers. 
Introduction to Boolean Algebra : Part 1
 Binary logic: True and false. Logical operators like OR, NOT, AND. Constructing truth tables. Basic postulates of Boolean Algebra. Logical addition, multiplication and complement rules. Principles of duality.  Basic theorems of boolean algebra: idempotence, involution, complementary, commutative, associative, distributive and absorption laws. 
Boolean Algebra : Part 2
De-morgan's laws. Logic gates. 2 input and 3 input gates. XOR, XNOR gates. Universality of NAND and NOR gates. Realization of Boolean expressions using NAND and NOR. Replacing gates in a boolean circuit with NAND and NOR.
  Understanding Karnaugh Maps : Part 1 Introducing Karnaugh Maps. Min-terms and Max-terms. Canonical expressions. Sum of products and product of sums forms. Shorthand notations. Expanding expressions in SOP and POS Forms ( Sum of products and Product of sums ). Minimizing boolean expressions via Algebraic methods or map based reduction techniques. Pair, quad and octet in the context of Karnaugh Maps.

Karnaugh Maps : Part 2
Map rolling. Overlapping and redundant groups. Examples of reducing expressions via K-Map techniques.
 Introduction to Combinational Circuits : Part 1
Combinational circuits: for which logic is entirely dependent of inputs and nothing else. Introduction to Multiplexers, De-multiplexers, encoders and decoders.Memories: RAM and ROM.  Different kinds of ROM - Masked ROM, programmable ROM. 
 Combinational Circuits : Part 2
 Static and Dynamic RAM, Memory organization.
Introduction to Sequential Circuits : Part 1 
Introduction to Sequential circuits. Different kinds of Flip Flops. RS, D, T, JK. Structure of flip flops. Switching example. Counters and Timers. Ripple and Synchronous Counters. 
Sequential Circuits : Part 2
ADC or DAC Converters and conversion processes. Flash Converters, ramp generators. Successive approximation and quantization errors. 
 


 










Tutorials in Basic Digital Electronics: At a glance
 

Introduction to the Number System : Part 1 
Introducing number systems. Representation of numbers in Decimal, Binary,Octal and Hexadecimal forms. Conversion from one form to the other.

Number System : Part 2 Binary addition, subtraction and multiplication. Booth's multiplication algorithm. Unsigned and signed numbers.

Introduction to Boolean Algebra : Part 1Binary logic: True and false. Logical operators like OR, NOT, AND. Constructing truth tables. Basic postulates of Boolean Algebra. Logical addition, multiplication and complement rules. Principles of duality. Basic theorems of boolean algebra: idempotence, involution, complementary, commutative, associative, distributive and absorption laws.

Boolean Algebra : Part 2De-morgan's laws. Logic gates. 2 input and 3 input gates. XOR, XNOR gates. Universality of NAND and NOR gates. Realization of Boolean expressions using NAND and NOR. Replacing gates in a boolean circuit with NAND and NOR.

 Understanding Karnaugh Maps : Part 1 Introducing Karnaugh Maps. Min-terms and Max-terms. Canonical expressions. Sum of products and product of sums forms. Shorthand notations. Expanding expressions in SOP and POS Forms ( Sum of products and Product of sums ). Minimizing boolean expressions via Algebraic methods or map based reduction techniques. Pair, quad and octet in the context of Karnaugh Maps.

Karnaugh Maps : Part 2 Map rolling. Overlapping and redundant groups. Examples of reducing expressions via K-Map techniques.

Introduction to Combinational Circuits : Part 1 Combinational circuits: for which logic is entirely dependent of inputs and nothing else. Introduction to Multiplexers, De-multiplexers, encoders and decoders.Memories: RAM and ROM. Different kinds of ROM - Masked ROM, programmable ROM.

Combinational Circuits : Part 2 Static and Dynamic RAM, Memory organization.

Introduction to Sequential Circuits : Part 1  Introduction to Sequential circuits. Different kinds of Flip Flops. RS, D, T, JK. Structure of flip flops. Switching example. Counters and Timers. Ripple and Synchronous Counters.

Sequential Circuits : Part 2
ADC or DAC Converters and conversion processes. Flash Converters, ramp generators. Successive approximation and quantization errors.


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