Understanding Number Systems: Decimal, Binary, Octal, and Hexadecimal, Slides of Digital Logic Design and Programming

Download Understanding Number Systems: Decimal, Binary, Octal, and Hexadecimal and more Slides Digital Logic Design and Programming in PDF only on Docsity!

Chapter 2

Number system

The numeric system we use daily is the decimal system

this system is not convenient for machines

the information is handled codified in the shape of on or off bits Numeric systems

Base (also called radix) = 10  Digit Position 2 1 0 -1 - Integer & fraction 5 1 2. 7 4  (^) Digit Weight Weight = (Base) Position^ 102 101 100. 10-1^10 - 5 1 2 7 4  Magnitude 500 10 2 0.7 0. Sum of “Digit x Weight” d 2 *B^2 +d 1 B^1 +d 0 B^0 +d-1B-1+d-2B-  (^) Formal Notation (512.74) 10 Decimal Number System

 (^) … a 5 a 4 a 3 a 2 a 1 a 0

. a - a - a - … Decimal point 5643 = 5 x 10 3

• 6 x 10 2
• 4 x 10 1
• 3 x 10 0 General form of base-r system

Binary Number System

Hexadecimal Number System

Number Systems

 (^210) (1024) is Kilo, denoted "K"  (^220) (1,048,576) is Mega, denoted "M"  (^230) (1,073, 741,824)is Giga, denoted "G" Special Powers of 2

Multiply the number by the ‘Base’ (=2)  Take the integer (either 0 or 1) as a coefficient  Take the resultant fraction and repeat the division Decimal (Fraction) to Binary Conversion

Decimal to Octal Conversion

16 = 2

Each group of 4 bits represents a hexadecimal digit

Works both ways (Binary to Hex &Hex to Binary) Binary − Hexadecimal Conversion

Convert to Binary as an intermediate step

Works both ways (Octal to Hex & Hex to Octal) Octal − Hexadecimal Conversion