Logic ..ch 1.pptx

Logic ..ch 1.pptx - E1121 DIGITAL LOGIC(A FALL 2017 Lecture...

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E1121 DIGITAL LOGIC (A) FALL 2017 Lecture 1 Number System

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Course information Lecture Schedule Sun. 10.45PM – 12.15PM Instructor Dr. Marwa Abdelrazik Elmenyawi [email protected] Office Hours: Sunday 9.00-10.30 PM. Teaching Assistants Eng. Nada Eng Eman Eng. Rehab
Chapter 1 Number Systems and Codes Computers and other digital systems process information as their Computers and other digital systems process information as their primary function. It is necessary to have methods and systems for representing information in forms that can be manipulated and stored using electronic or other types of hardware.

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Outline of Chapter 1 Number Systems Number-base Conversions Arithmetic Operations Complements Signed Binary Numbers Binary Codes
Outline of Chapter 1 Number Systems Number-base Conversions Arithmetic Operations Complements Signed Binary Numbers Binary Codes

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Introduction to Numbering Systems We are all familiar with the decimal number system (Base 10). Some other number systems that we will work with are: Binary Octal Hexadecimal 1
Binary numbers? Computers work only on two states On Off Basic memory elements hold only two states Zero / One Thus a number system with two elements {0,1} A binary digit – bit ! 2

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Octal & Hexadecimal System 8 Computer scientists are often looking for shortcuts to do things One of the ways in which we can represent binary numbers is to use their octal equivalents instead This is especially helpful when we have to do fairly complicated tasks using numbers 3
Numbers Each number system is associated with a base or radix For example: The decimal number system is said to be of base or radix 10 A number in base r contains r digits 0,1,2,...,r-1 Decimal (Base 10): 0,1,2,3,4,5,6,7,8,9 Numbers are usually expressed in positional notation MSD: most significant digit LSD: least significant digit 4

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Characteristics of Numbering Systems 1) The digits are consecutive. 2) The number of basic digits is equal to the size of the base. 3) Zero is always the first digit. 4) The base number is never a digit. 5) When 1 is added to the largest basic digit, a sum of zero and a carry of one results. 6) Numeric values are determined by the implicit positional values of the digits. 5
Common Number Systems System Base Basic digit Used by humans? Used in computers? Decimal 10 0, 1, … 9 Yes No Binary 2 0, 1 No Yes Octal 8 0, 1, … 7 No No Hexa- decimal 16 0, 1, … 9, A, B, … F No No 6

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Decimal Binary Octal Hex 00 0000 00 0 01 0001 01 1 02 0010 02 2 03 0011 03 3 04 0100 04 4 05 0101 05 5 06 0110 06 6 07 0111 07 7 08 1000 10 8 09 1001 11 9 10 1010 12 A 11 1011 13 B 12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F 16 10000 20 10 17 10001 21 11 Quantities/Counting 7
Outline of Chapter 1 Number Systems Number-base Conversions Arithmetic Operations Complements Signed Binary Numbers Binary Codes

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Bridging the Digital Divide 00100 0101011 10101 010 10010 1101 011011 1101 010 00101101 00100 0101011 011011 1101 00101101 00100 001011 10101 010 10010 1101 011011 1101 010 00101101 00100 01010 11 011011 1101 00101 10010 10010 00101101 Binary-to-Decimal Conversion Decimal-to-Binary Conversion 8
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• Spring '18
• dr.marwa el manyawy
• Logic, Binary numbers, Binary numeral system

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