PPT-Data Representation – Binary Numbers

  Integer Conversion Between Decimal and Binary Bases Task accomplished by Repeated division of decimal number by 2 integer part of decimal number Repeated multiplication of decimal number by 2 fractional part of decimal number. brPage 3br 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 01 A binary digit bit brPage 4br Decimal numbers 1439 1 x 10 4 x 10 3 x 10 9 x Converting. Decimal to Binary. Binary to Decimal. Base-Ten Place-Value System. The sleek efficient number system we know today is called the base-ten number system or Hindu-Arabic system. It was first developed by the Hindus and Arabs. This used the best features from several of the systems we mentioned before.. 350151 – Digital Circuit 1. Choopan. . Rattanapoka. Representing Negative Numbers in Binary. Up to this point, we have not been discussed how to represent negative numbers in binary.. Ex: 5. 10. – 7. Binary . Representation for Numbers. Assume 4-bit numbers. 5 as an integer. 0101. -5 as an integer. How?. 5.0 . as a . real number. How?. What about 5.5?. Sign Bit. R. eserve the most-significant bit to indicate sign. ICS 6D. Sandy . Irani. Number representation. Our number system represents numbers in base 10 (also called decimal notation). Each place represents a power of 10:. 3045 = . 3. ·. 10. 3. + . 0. ·. The arithmetic used by computers differs in some ways from that used by people.. Computers perform operations on numbers with finite and fixed precision.. Computers use the binary rather than the decimal system for representing numbers.. in . Computer . Systems. Chapter 2. 2. Chapter 2 Objectives. Understand the fundamentals of numerical data representation and manipulation in digital computers.. Master the skill of converting between various radix systems.. Prof. Hakim Weatherspoon. CS 3410, Spring 2015. Computer Science. Cornell University. See: P&H Chapter 2.4, 3.2, B.2, B.5, B.6. Big Picture: Building a Processor. PC. imm. memory. target. offset. Decimal. . vs. Binary. = 1001. = 101. = 10. 1 = on =. 0 = off = . On and off. Creating a decimal number 
from a binary number. STAGE 1. The decimal number is ________. Creating decimal 
from binary. Unit 1. 2. This chapter in the book includes:. Objectives. Study Guide. 1.1 Digital Systems and Switching Circuits. 1.2 Number Systems and Conversion. 1.3 Binary Arithmetic. 1.4 Representation of Negative Numbers. why used. conversions, including to/from decimal. negative binary numbers. floating point numbers. character codes . Lubomir Bic. 1. Radix Number Systems. basic idea of a radix number system --. how do we count:. What is binary?. You and I write numbers like this: twelve is 12, sixty eight is 68, and one hundred is 100. Binary is a . number system . that computers use. That is, binary is the way that computers express numbers.. &. Binary to Denary. Chapter . 4 . Data Representation. Units. Bit – 1 bit. Nibble – 4 bits. Byte – 8 bits. Kilobyte – 1024 bytes or 1024x8 bits. Megabyte – 1024 kilobytes. Gigabyte – 1024 megabytes. 6. 9. 2. 4. 1. 8. <. >. =. © 2014 Goodrich, Tamassia, Goldwasser. Presentation for use with the textbook . Data Structures and Algorithms in Java, 6. th. edition. , by M. T. Goodrich, R. Tamassia, and M. H. Goldwasser, Wiley, 2014.