Chapter 3 Data Representation. Dr. Bernard Chen Ph.D. University of Central Arkansas Spring 2009. Data Types. The data types stored in digital computers may be classified as being one of the following categories: numbers used in arithmetic computations,

ByReview on Number Systems. Decimal, Binary, and Hexadecimal. Base-N Number System. Base N N Digits: 0, 1, 2, 3, 4, 5, …, N-1 Example: 1045 N Positional Number System . Digit d o is the least significant digit (LSD). Digit d n -1 is the most significant digit (MSD).

ByBinary Subtraction. Section 3-9 Mano & Kime. Binary Subtraction. Review from CSE 171 Two’s Complement Negative Numbers Binary Adder-Subtractors 4-bit Adder/Subtractor in VHDL. A . 0 . D . 0 . B . 0 . C . 1 . Half Subtractor. A . B . D . C . 0 . 0 . 0 . 1 . 0 0 0 0

ByBinary Arithmetic. Everything a computer does is based on mathematical equations But computers can only carry out simple functions So the equations have to worked out in terms of what the computer is capable of

ByArithmetic Functions and HDLs. Chapter 4. Half adder. X +Y ----- CS. Full adder. X Y +Z ----- CS. Binary ripple carry adder. Binary subtraction (for unsigned binary number). 11100 ( 借位 ) 10011 ( 被減數 ) - 1 1110 ( 減數 ) ---------------------------------

ByLogic and Sequential Circuit Design (EC – 201) . Textbook. Digital Logic and Computer Design by M. Morris Mano (Jan 2000 ). Topics.

ByTK 2633: Microprocessor & Interfacing. Lecture 5: Arithmetic and Logic Instructions. OBJECTIVES. Explain the operation of the 8085 arithmetic and logic instructions and describe their effect on the flag bits. Describe how DAA adjusts the result of a BCD addition.

ByBBO/Decigo and the Neutron-Star-Binary Subtraction Problem C.Cutler & J.Harms, PRD 73, 04200 (2006). --from Smith et al., astro-ph/0506422. Why go to shorter arms, or higher frequency ?. Ans: to escape the WD-WD foreground.

ByNegative Binary Numbers. In decimal we are quite familiar with placing a “-” sign in front of a number to denote that it is negative The same is true for binary numbers a computer won’t understand that What happens in memory then?. Binary Negative Numbers. There are several representations

ByBinary Math. CS208. Decimal Addition Example. 3 7 5 8 + 4 6 5 7. 1) Add 8 + 7 = 15 Write down 5 , carry 1. Add 3758 to 4657 :. 2) Add 5 + 5 + 1 = 11 Write down 1 , carry 1. 1. 1. 1. 3) Add 7 + 6 + 1 = 14 Write down 4 , carry 1. 8. 4. 1. 5.

ByArithmetic circuits. Binary addition Binary Subtraction Unsigned binary numbers Sign-magnitude numbers 2 ’ S Complement representation 2 ’ S Complement arithmetic Arithmetic building blocks. Powers of 2 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15

ByBinary Operations. Math/Logical. Binary Math. Decimal Addition Example. 3 7 5 8 + 4 6 5 7. 1) Add 8 + 7 = 15 Write down 5 , carry 1. Add 3758 to 4657 :. 2) Add 5 + 5 + 1 = 11 Write down 1 , carry 1. 1. 1. 1. 3) Add 7 + 6 + 1 = 14 Write down 4 , carry 1. 8. 4.

ByBinary Subtraction. borrow. -). Subtracter. A. R. Subtracter. B. b. Arithmetic: Subtraction. 293 – 154 = 139. 293 – 154 = 293 + ( -154). 293 – 154 = 293 + ( 1,000,000 - 154) - 1,000,000. ( 1,000,000 - 154) = 999,846. 099,999 +) 900,000 999,999. +). Positive:

ByCombinational Logic Design: Substractor. Overview. Binary Subtraction 2’ ’s complement Extension to r’ s complement Subtraction with complements Binary Adders/Subtractors Signed numbers Signed Addition/Subtraction Overflow problem Binary Multipliers.

ByNegative Binary Numbers. In decimal we are quite familiar with placing a “-” sign in front of a number to denote that it is negative The same is true for binary numbers a computer won’t understand that What happens in memory then?. Binary Negative Numbers. There are several representations

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