Computer Number System
understand only numbers. A computer can understand positional number system where there are only a few symbols called digits and these symbols represent
number system.pdf
Computer architecture supports following number systems. •. Binary number system. •. Octal number system. •. Decimal number system.
Lecture #2: Binary Hexadecimal
https://personal.utdallas.edu/~dodge/EE2310/lec2.pdf
Computer Fundamentals: Number Systems Dr Robert Harle
Number systems (decimal binary
INTRODUCTION TO COMPUTER SYSTEM
They also perform arithmetic and logical operations on alphabetic numeric and other types of information. This information provided by the user to the computer
1. Number System
Number Systems - Binary Numbers - Number base conversions - Octal and Hexa Decimal Numbers - The block diagram of digital computer is given below:.
1 Number System (Lecture 1 and 2 supplement)
the basic number system for all computers. In positional number systems a number is represented by a string of digits where the position of each digit is
Computer fundamental (Tutorial Point)
This tutorial explains the foundational concepts of computer hardware software
Numbering Systems Tutorial What is it? Decimal System
Computers use binary system binary system uses 2 digits: 0
ASSEMBLY LANGUAGE TUTORIAL - Simply Easy Learning by
Assembly language is a low-level programming language for a computer or other hexadecimal number system represents a binary data by dividing each byte ...
Number Systems Base Conversions and Computer Data
Number Systems Base Conversions and Computer Data Representation Decimal and Binary Numbers When we write decimal (base 10) numbers we use a positional notation system Each digit is multiplied by an appropriate power of 10 depending on its position in the number: For example: 2843 = 8 x 10 + 4 x 101 + 3 x 100 = 8 x 100 + 4 x 10 + 3 x 1
Number Systems Base Conversions and Computer Data
Decimal Numbering System Ten symbols: 0 1 2 3 4 5 6 7 8 9 Represent larger numbers as a sequence of digits • Each digit is one of the available symbols Example: 7061 in decimal (base 10) • 706110 = (7x 103) + (0x 102) + (6x 101) + (1x 100) Octal Numbering System Eight symbols:: 0 1 2 3 4 5 6 7
Computer Number System - Online Tutorials Library
Number System and Description Binary Number System Base 2 Digits used : 0 1 2 Octal Number System Base 8 Digits used : 0 to 7 3 Hexa Decimal Number System Base 16 Digits used : 0 to 9 Letters used : A- F Binary Number System Characteristics of binary number system are as follows: Uses two digits 0 and 1 Also called base 2 number system
Number Systems and Number Representation - Princeton University
• The binary hexadecimal and octal number systems • Finite representation of unsigned integers • Finite representation of signed integers • Finite representation of rational (floatingpoint) numbers-Why? • A power programmer must know number systems and data representation to fully understand C’s primitive data types Primitive
Computer Fundamentals: Number Systems Dr Robert Harle
Computer Fundamentals: Number Systems Dr Robert Harle Computer Fundamentals:Number Systems Dr Robert Harle Today's Topics The significance of the bit and powers of 2 Data quantities (B kB MB GB etc) Number systems (decimal binary octal hexadecimal) Representing negative numbers (sign-magnitude 1’s complement 2’s complement)
Searches related to number system in computer tutorial pdf filetype:pdf
The study of number systems is useful to the student of computing due to the fact that number systems other than the familiar decimal (base 10) number system are used in the computer field Digital computers internally use the binary (base 2) number system to represent data and perform arithmetic calculations The
[PDF] NUMBER SYSTEM CONVERSIONS - ipsgwaliororg
Number systems are the technique to represent numbers in the computer system architecture A Binary number system has only two digits that are 0 and 1
[PDF] Number Systems Tutorial - The VB Programmer
The study of number systems is useful to the student of computing due to the fact that number systems other than the familiar decimal
[PDF] Computer Number System - Tutorialspoint
A computer can understand positional number system where there are only a few symbols called digits 1 Binary Number System Base 2 Digits used : 0 1
[PDF] The Computer Number System - The University of Texas at Dallas
N B Dodge 9/16 1 Lecture #2: Binary Hexadecimal and Decimal Numbers Binary Numbers – The Computer Number System • Number systems are simply ways to
[PDF] Computer Fundamentals: Number Systems Dr Robert Harle
Number systems (decimal binary octal hexadecimal) ? Representing negative numbers (sign-magnitude 1's complement 2's complement)
[PDF] 1 Number System - Sathyabama
Number Systems - Binary Numbers - Number base conversions - Octal and Hexa Decimal Numbers - Complements - Signed Binary Numbers - Binary Arithmetic - Binary
(PDF) Number System - ResearchGate
27 oct 2017 · Abstract · 1) Binary Number System A Binary number system has only two digits which are 0 and 1 Every number (value) is · 2) Octal number
[PDF] Number System (Lecture 1 and 2 supplement)
the basic number system for all computers In positional number systems a number is represented by a string of digits where the position of each digit is
[PDF] Number System and Conversion
The decimal system is the number system that we use 0 and 1 ? Hexadecimal System uses sixteen symbols 0 1 2 3 4 5 6 7 8 9 A B C D E F
[PDF] Chapter 3-Number System - BCA Notes
Computer Fundamentals: Pradeep K Sinha Priti Sinha Slide 5/40 Chapter 3: Number Systems Ref Page § Characteristics § Use symbols such as I for 1
How many digits are there in a decimal number system?
- In the decimal number system, there are ten possible values that can appear in each digit position, and so there are ten numerals required to represent the quantity in each digit position. The decimal numerals are the familiar zero through nine (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). In a positional notation system, the number base is called the radix.
How many digits are in the base-16 hexadecimal number system?
- The Hexadecimal Number System The base-16 hexadecimal number system has 16 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F).
How do you interpret a binary number?
- In a binary number being interpreted using the two’s complement representation, the high order bit of the number indicates the sign. If the sign bit is 0, the number is positive, and if the sign bit is 1, the number is negative. For positive numbers, the rest of the bits hold the true magnitude of the number.
How many bits are in a computer?
- In most computer systems, this isn’t the case. Numbers in computers are typically represented using a fixed number of bits. These sizes are typically 8 bits, 16 bits, 32 bits, 64 bits and 80 bits. These sizes are generally a multiple of 8, as most computer memories are organized on an 8 bit byte basis.
Computer Fundamentals:
Number Systems
Dr Robert Harle
Today's Topics
yThe significance of the bit and powers of 2 yData quantities (B, kB, MB, GB, etc) yNumber systems (decimal, binary, octal , hexadecimal) yRepresenting negative numbers (sign-magnitude, 1's complement, 2's complement) yBinary addition (carries, overflows) yBinary subtraction So... yWhat is a bit?The Significance of the Bit
yA bit (Binary digIT) is merely 0 or 1 yIt is a unit of information since you cannot communicate with anything less than two states yThe use of binary encoding dates back to the 1600s with Jacquard's loom, which created textiles using card templates with holes that allowed needles throughBits and Computers
yThe nice thing about a bit is that, with only two states, it is easy to embody in physical machinery yEach bit is simply a switch and computers moved from vacuum tubes to transistors for this e-Decimal Number System
yMost computers count in binary, which we can easily understand from the decimal so ingrained in us 35462Decimal Number System
yMost computers count in binary, which we can easily understand from the decimal so ingrained in us354622x100
Decimal Number System
yMost computers count in binary, which we can easily understand from the decimal so ingrained in us354622x1006x101+
Decimal Number System
yMost computers count in binary, which we can easily understand from the decimal so ingrained in us354622x1006x101+4x102+
Decimal Number System
yMost computers count in binary, which we can easily understand from the decimal so ingrained in us354622x1006x101+4x102+5x103+
Decimal Number System
yMost computers count in binary, which we can easily understand from the decimal so ingrained in us354622x1006x101+4x102+5x103+3x104+
Binary
yBinary is exactly the same, only instead of ten digits/states (0 to 9) we have just two, so the base becomes 2:101100x201x21+1x22+0x23+1x24+
Binary
yBinary is exactly the same, only instead of ten digits/states (0 to 9) we have just two, so the base becomes 2:10110b = 22d0x201x21+1x22+0x23+1x24+
Binary
yBinary is exactly the same, only instead of ten digits/states (0 to 9) we have just two, so the base becomes 2:10110b = 22d0x201x21+1x22+0x23+1x24+
Most Signiificant
Bit (MSB)Least Signiificant
Bit (LSB)
Works for Fractional Numbers too...
35.4622x10-36x10-2+4x10-1+5x100+3x101+
Works for Fractional Numbers too...
10.110b = 2.75d0x2-31x2-2+1x2-1+0x20+1x21+35.4622x10-36x10-2+4x10-1+5x100+3x101+
Check11.011b
Check11.011b = 3.375d1x2-31x2-2+0x2-1+1x20+1x21+
Representable Numbers
yWith d decimal digits, we can represent 10d different values, usually the numbers 0 to (10d-1) inclusive yIn binary with n bits this becomes 2n values, usually the range 0 to (2n-1) yComputers usually assign a set number of bits (physical switches) to an instance of a type. yAn integer is often 32 bits, so can represent positive integers from 0 to 4,294,967,295 incl. yOr a range of negative and positive integers...Other Common Bases
yHigher bases make for shorter numbers that are easier for humans to manipulate. e.g.6654733d=11001011000101100001101b
yWe traditionally choose powers-of-2 bases because this corresponds to whole chunks of binaryOther Common Bases
yHigher bases make for shorter numbers that are easier for humans to manipulate. e.g.6654733d=11001011000101100001101b
yWe traditionally choose powers-of-2 bases because this corresponds to whole chunks of binary yOctal is base-8 (8=23 digits, which means 3 bits per digit) y6654733d=011-001-011-000-101-100-001-101b= 31305415oOther Common Bases
yHigher bases make for shorter numbers that are easier for humans to manipulate. e.g.6654733d=11001011000101100001101b
yWe traditionally choose powers-of-2 bases because this corresponds to whole chunks of binary yOctal is base-8 (8=23 digits, which means 3 bits per digit) y6654733d=011-001-011-000-101-100-001-101b= 31305415o yHexadecimal is base-16 (16=24 digits so 4 bits per digit) yOur ten decimal digits aren't enough, so we add 6 new ones: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,FOther Common Bases
yHigher bases make for shorter numbers that are easier for humans to manipulate. e.g.6654733d=11001011000101100001101b
yWe traditionally choose powers-of-2 bases because this corresponds to whole chunks of binary yOctal is base-8 (8=23 digits, which means 3 bits per digit) y6654733d=011-001-011-000-101-100-001-101b= 31305415o yHexadecimal is base-16 (16=24 digits so 4 bits per digit) yOur ten decimal digits aren't enough, so we add 6 new ones: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F yBecause we constantly slip between binary and hex, we have a special marker for it yPrefix with '0x' (zero-x). So 0x658B0D=6654733d, 0x123=291d Bytes yA byte was traditionally the number of bits needed to store a character of text yA de-facto standard of 8 bits has now emerged y256 values y0 to 255 incl. yTwo hex digits to describe y0x00=0, 0xFF=255 yCheck: what does 0xBD represent? Bytes yA byte was traditionally the number of bits needed to store a character of text yA de-facto standard of 8 bits has now emerged y256 values y0 to 255 incl. yTwo hex digits to describe y0x00=0, 0xFF=255 yCheck: what does 0xBD represent? yB → 11 or 1011 yD → 13 or 1101 yResult is 11x161+13x160 = 189 or 10111101Larger Units
yStrictly the SI units since 1998 are: yKibibyte (KiB) y1024 bytes (closest power of 2 to 1000) yMebibyte (MiB) y1,048,576 bytes yGibibyte (GiB) y1,073,741,824 bytesLarger Units
yStrictly the SI units since 1998 are: yKibibyte (KiB) y1024 bytes (closest power of 2 to 1000) yMebibyte (MiB) y1,048,576 bytes yGibibyte (GiB) y1,073,741,824 bytes ybut these haven't really caught on so we tend to still use the SI Kilobyte, Megabyte, Gigabyte. This leads to lots of confusion since technically these are multiples of 1,000.The Problem with Ten
Unsigned Integer Addition
yAddition of unsigned integers works the same way as addition of decimal (only simpler!) y0 + 0 = 0 y0 + 1 = 1 y1 + 0 = 1 y1 + 1 = 0, carry 1 yOnly issue is that computers have fixed sized types so we can't go on adding forever... 111+ 001001 + 001
Carry lflag:Carry lflag:
Modulo or Clock Arithmetic
yOverflow takes us across the dotted boundary ySo 7+1=0 (overflow) yWe say this is (7+1) mod 8 000 001 010011100101110111000
001 010 011 100101
110
111
Negative Numbers
yAll of this skipped over the need to represent negatives. yThe naïve choice is to use the MSB to indicate +/- y1 in the MSB → negative y0 in the MSB → positive yThis is the sign-magnitude technique-7 = 1111NegativeNormal positive
representation of 7Difficulties with Sign-Magnitude
yHas a representation of minus zero (10002=-0) so wastes one of our 2n labels yAddition/subtraction circuitry must be designed from scratch 1101+ 0001 1110
Our unsigned addition alg.
Difficulties with Sign-Magnitude
yHas a representation of minus zero (10002=-0) so wastes one of our 2n labels yAddition/subtraction circuitry must be designed from scratch 1101+ 0001 1110
Our unsigned addition alg.+13
+1 +14Unsigned
interpretationDifficulties with Sign-Magnitude
yHas a representation of minus zero (10002=-0) so wastes one of our 2n labels yAddition/subtraction circuitry must be designed from scratch 1101+ 0001
1110-5
+1 -6+13 +1 +14Sign-mag
interpretationUnsigned interpretationOur unsigned addition alg.
Alternatively...
yGives us two discontinuities and a reversal of direction using normal addition circuitry!! 000 001 010011100101110111000
001 010 011 100101
110
111
Ones' Complement
yThe negative is the positive with all the bits flipped y7 → 0111 so -7 → 1000 yStill the MSB is the sign yOne discontinuity but still -0 :-( 000 001 010011100101110111000
001 010 011 100101
110
111
Two's Complement
yThe negative is the positive with all the bits flipped and 1 added (the same procedure for the inverse) y7 → 0111 so -7 → 1000+0001 → 1001 yStill the MSB is the sign yOne discontinuity and proper ordering 000 001 010 011 100101
110
111
000 001 010
011100101110111
Two's Complement
yPositive to negative: Invert all the bits and add 1 yNegative to positive: Same procedure!!1011 (-5) → 0100 → 0101 (+5)0101 (+5) → 1010 → 1011 (-5)
Signed Addition
1101+0001 1110
Our unsigned addition alg.y...it just works with our addition algorithm! +13 +1 +14
Unsigned
Signed Addition
1101+0001
1110-3
+1 -2+13 +1 +142's-compUnsigned
Our unsigned addition alg.y...it just works with our addition algorithm!Signed Addition
1101+0001
1110-3
+1 -2+13 +1 +142's-compUnsigned
Our unsigned addition alg.y...it just works with our addition algorithm! ySo we can use the same circuitry for unsigned and 2s- complement addition :-) yWell, almost.Signed Addition 0100+0100
1000+4
+4 +8UnsignedCarry lflag: 0
ySo we can use the same circuitry for unsigned and 2s- complement addition :-) yWell, almost. yThe problem is our MSB is now signifying the sign and our carry should really be testing the bit to its right :-(Signed Addition 0100+0100
1000+4
+4 -8+4 +4 +82's-compUnsignedCarry lflag: 0
ySo we can use the same circuitry for unsigned and 2s- complement addition :-) yWell, almost. yThe problem is our MSB is now signifying the sign and our carry should really be testing the bit to its right :-( ySo we introduce an overflow flag that indicates this problemSigned Addition 0100+0100
1000+4
+4 -8+4 +4 +82's-compUnsignedCarry lflag: 0
Overlflow: 1
Integer subtraction
yCould implement the "borrowing" algorithm you probably learnt in school yBut why bother? We can just add the2's complement instead.
0100- 0011 0100
+1101
0001→
Flags Summary
yWhen adding/subtracting yCarry flag → overflow for unsigned integer yOverflow flag → overflow for signed integer yThe CPU does not care whether it's handling signed or unsigned integers yDown to our compilers/programs to interpret the resultFractional Numbers
yScientific apps rarely survive on integers alone, but representing fractional parts efficiently is complicated. yOption one: fixed point ySet the point at a known location. Anything to the left represents the integer part; anything to the right the fractional part yBut where do we set it?? yOption two: floating point yLet the point 'float' to give more capacity on its left or right as needed yMuch more efficient, but harder to work with yVery important: more in Numerical Methods courseComputer Fundamentals:
Number Systems
Dr Robert Harle
Today's Topics
yThe significance of the bit and powers of 2 yData quantities (B, kB, MB, GB, etc) yNumber systems (decimal, binary, octal , hexadecimal) yRepresenting negative numbers (sign-magnitude, 1's complement, 2's complement) yBinary addition (carries, overflows) yBinary subtraction So... yWhat is a bit?The Significance of the Bit
yA bit (Binary digIT) is merely 0 or 1 yIt is a unit of information since you cannot communicate with anything less than two states yThe use of binary encoding dates back to the 1600s with Jacquard's loom, which created textiles using card templates with holes that allowed needles throughBits and Computers
yThe nice thing about a bit is that, with only two states, it is easy to embody in physical machinery yEach bit is simply a switch and computers moved from vacuum tubes to transistors for this e-Decimal Number System
yMost computers count in binary, which we can easily understand from the decimal so ingrained in us 35462Decimal Number System
yMost computers count in binary, which we can easily understand from the decimal so ingrained in us354622x100
Decimal Number System
yMost computers count in binary, which we can easily understand from the decimal so ingrained in us354622x1006x101+
Decimal Number System
yMost computers count in binary, which we can easily understand from the decimal so ingrained in us354622x1006x101+4x102+
Decimal Number System
yMost computers count in binary, which we can easily understand from the decimal so ingrained in us354622x1006x101+4x102+5x103+
Decimal Number System
yMost computers count in binary, which we can easily understand from the decimal so ingrained in us354622x1006x101+4x102+5x103+3x104+
Binary
yBinary is exactly the same, only instead of ten digits/states (0 to 9) we have just two, so the base becomes 2:101100x201x21+1x22+0x23+1x24+
Binary
yBinary is exactly the same, only instead of ten digits/states (0 to 9) we have just two, so the base becomes 2:10110b = 22d0x201x21+1x22+0x23+1x24+
Binary
yBinary is exactly the same, only instead of ten digits/states (0 to 9) we have just two, so the base becomes 2:10110b = 22d0x201x21+1x22+0x23+1x24+
Most Signiificant
Bit (MSB)Least Signiificant
Bit (LSB)
Works for Fractional Numbers too...
35.4622x10-36x10-2+4x10-1+5x100+3x101+
Works for Fractional Numbers too...
10.110b = 2.75d0x2-31x2-2+1x2-1+0x20+1x21+35.4622x10-36x10-2+4x10-1+5x100+3x101+
Check11.011b
Check11.011b = 3.375d1x2-31x2-2+0x2-1+1x20+1x21+
Representable Numbers
yWith d decimal digits, we can represent 10d differentquotesdbs_dbs20.pdfusesText_26[PDF] number theory congruence problems and solutions
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