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Binary Representation and Computer Arithmetic

Aug 04, 2012

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Binary Representation and Computer Arithmetic

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1. Binary Representation and Computer Arithmetic

2. DECIMAL and BINARY system The Decimal System This uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to represent numbers The Binary System uses just two digits, 0 and 1 easier for a computer to distinguish between two different voltage levels (than ten)

3. POSITIONAL NOTATION (in decimal)

Binary and Floating Point Arithmetic

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Binary Arithmetic

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Registers and Binary Arithmetic

Prof. Sirer COMP 303 Ko ç University. Registers and Binary Arithmetic. Recap. We can build combinatorial circuits Gates, Karnaugh maps, minimization We can build stateful circuits Record 1-bit values in latches and flip-flops Powerful combination We can build real, useful devices

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Computer Arithmetic

Computer Arithmetic. See Stallings Chapter 9. Arithmetic &amp; Logic Unit (ALU). ALU does the calculations “Everything else in the computer is there to service this unit” (!) Handles integers May handle floating point (real) numbers

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Binary representation and logic

Binary representation and logic. bit - binary digit - 0/1, off/on binary devices are relatively easy to build mathematical diversion: assume an n-state device where the cost of the device is linear in n (= kn ); the number of devices required for

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Binary Representation

Binary Representation. 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 Consider integers in 4 bits

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Binary Arithmetic

Binary 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

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Arithmetic and Data Representation

Arithmetic and Data Representation. http://www.pds.ewi.tudelft.nl/~iosup/Courses/2011_ti1400_3.ppt. Lecture 1 Making functions. nand gates. A. Y. ADD. B. Y. A,B. . time. 2. Lecture 1 Making functions. Circuit Diagram http://xkcd.com/730/. Lecture 2 Programmable device.

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Number Representation and Binary Arithmetic

Number Representation and Binary Arithmetic. Unsigned Addition. Binary Addition. 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 and carry 1 to the next column. Examples:. Carries. 1 1 1 0101 (5 10 ) + 0011 (3 10 ) 1000 (8 10 ). 0101 (5 10 ) + 0010 (2 10 )

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Binary numbers and arithmetic

Binary numbers and arithmetic. addition. Addition (decimal). Addition (binary). Addition (binary). Addition (binary). So can we count in binary?. Counting in binary (4 bits). 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15. 0000 0001 …. multiplication. Multiplication (decimal).

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Binary Arithmetic

Binary Arithmetic. Binary Addition. Example 1: 0 1 0 1 + 0 1 1 0. Addition Rules:. 1. 0 + 0 = 0 + 1 = 1 + 0 = 1 + 1 = 1 + 1 + 1 =. 0. 1. 1. 1. 0. 1. 1. 0 carry 1. 1 carry 1. Example 2: 1 0 1 1 1 + 1 0 0 1 0. 1. 1. 1. 0. 1. 0. 0. 1. OVERFLOW.

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Binary Arithmetic

Binary Arithmetic. Math For Computers. Huh?. Binary numbers are NUMBERS That means you can add, subtract, multiply, and divide 2 + 2 = 4 In Binary: 10 + 10 = 100 So you COULD just convert all numbers to decimal, do the math, and then convert the answer back… But I don’t care about the math

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Binary Arithmetic

Binary Arithmetic. Kuliah Sistem Digital, Teknik Elektro UMY (Rahmat Adiprasetya). Introduction.

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Computer Arithmetic and the Arithmetic Unit

Computer Arithmetic and the Arithmetic Unit. Lesson 2 - Ioan Despi. Digital Number Systems. Digital number systems have a base or radix b Using positional notation , an m-digit base b number is written x = x m-1 x m-2 ... x 1 x 0 0  x i  b-1, 0  i &lt; m

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Binary Representation and Computer Arithmetic

Binary Representation and Computer Arithmetic. DECIMAL and BINARY system. The Decimal System This uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to represent numbers The Binary System uses just two digits, 0 and 1

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Binary Representation

Binary Representation. The basis of all digital data is binary representation. Binary - means ‘two’ 1, 0 True, False Hot, Cold On, Off We must be able to handle more than just two values for real world problems 1, 0, 56 True, False, Maybe Hot, Cold, Lukewarm, Cool On, Off, Leaky.

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Binary Arithmetic

Binary Arithmetic. Numbers Inside the Computer. Counting. There are many different ways of writing numbers 1,2,3,4,5,6,7,8,9,10,11 … I,II,III,IV,V,VI,VII,VIII,IX,X,XI … Etc. One of the earliest ways of writing numbers was like this:. Number Systems.

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Binary Arithmetic

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Arithmetic operations in binary

Arithmetic operations in binary. Addition / subtraction 01011 + 111 ? “Method” exatly the same as decimal. Arithmetic operations in binary. Addition X = x n … x i … x 0 + Y = y n … y i … y 0 __________________ d i d i = (x i + y i ) mod r + carry-in.

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Binary Arithmetic

Binary Arithmetic. Adding Binary numbers Overflow conditions How does it all work? AND, OR and NOT. Decimal Addition. You are probably already familiar with adding decimal numbers. 7 +2 9. 5 +1 6. 2 +3 5.

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Binary Representation

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