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Lecture #2 - Number Systems and Binary Arithmetic

# Lecture #2 - Number Systems and Binary Arithmetic - ECE 301...

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Unformatted text preview: ECE 301 – Digital System Design Number Systems and Binary Arithmetic (Lecture #2) Learning Objectives • Number Systems – Binary, octal, and hexadecimal • Conversion between number systems • Binary arithmetic – Addition, subtraction, and multiplication • Representation of negative numbers Spring 2012 ECE 301 - Digital 2 Reading Roth & Kinney, Sections 1.1 – 1.4 Spring 2012 ECE 301 - Digital 3 Number Systems Spring 2012 ECE 301 - Digital 4 Number Systems What is the value of the following number: 1101001.010 Spring 2012 ECE 301 - Digital 5 Number Systems • Every number system is defined by its radix . • R is the radix (or base ) of a number system. – Must be positive. – R digits in the number system: [0, .. , R-1] Spring 2012 ECE 301 - Digital 6 Number Systems Which number system(s) are important to the digital circuit designer? Spring 2012 ECE 301 - Digital 7 Spring 2012 ECE 301 - Digital 8 Number Systems The number systems that are important to the digital system designer are: Binary (base 2) [0,1] Octal (base 8) [0 … 7] Hexadecimal (base 16) [0 … 9, A … F] Other number systems You must, however, be familiar with other Spring 2012 ECE 301 - Digital 9 Number Systems A number is written in positional notation : And it's decimal value is determined using the power series expansion : [anan-1 … a2a1a0.a-1a-2 … a-m]R an x Rn + an-1 x Rn-1 + … + a0 x R0 + a-1 x R-1 + … a-m x R-m Spring 2012 ECE 301 - Digital 10 Number Systems: Examples Determine the decimal equivalent value of: 1101.012 (binary) A36.E16 (hexadecimal) = 1 x 23 + 1 x 22 + 1 x 20 + 1 x 2-2 = 13.2510 = 10 x 162 + 3 x 161 + 6 x 160 + 14 x 16-1 = 2790.87510 Spring 2012 ECE 301 - Digital 11 Number Systems: Exercises Determine the decimal equivalent value for each of the following numbers: – 101101.012 (binary) – 436.58 (octal) – B4C.916 (hexadecimal) – 12213 (base 3) Spring 2012...
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Lecture #2 - Number Systems and Binary Arithmetic - ECE 301...

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