ECE III SEM BINARY CODES
Manav Rachna University Manav Rachna College of Engineering BINARY CODES Electronic digital systems use signals that have two distinct valuesand circuit elements that have two stable states. There is a direct analogy among binary signals, binary circuitelements, and binary digits. A binary number of n digits, for example,may be represented by n binary circuit elements, each having anoutput signal equivalent to a 0 or a 1. Digital systems represent and manipulate not only binary numbers,but also many other discrete elements of information. Any discrete element of information distinct among a group ofquantities can be represented by a binary code. For example, red isone distinct color of the spectrum. The letter A is one distinct letter ofthe alphabet. A bit, by definition, the binary digit. When used in conjunction with abinary code, it is better to think of it as denoting a binary quantityequal to 0 or 1. To represent a group of 2n distinct elements in a binary code requiresa minimum ofn bits. This is because it is possible to arrange n bits in2n distinct ways. For example, a group of four distinct quantities can be represented bya two-bit code, with each quantity assigned one of the following bitcombinations: 00, 01, 10, 11. Manav Rachna University A group of eight elements requires a three-bit code, with eachelement assigned to one of the following: 000, 001, 010, 011,100, 101, 110, 111. The examples show that the distinct bit combinations ofan n- bit code can be found by counting in binary from 0 to (2n-1).Some bit combinations of n-bit code can be found by the numberof elements of the group to be coded is not a multiple of thepower of2. The ten decimal digits 0, 1, 2, 3, ., 9 are anexample of such a group. A binary code that distinguishes among ten elements mustcontain at least four bits; three bits can distinguish a maximumof eight elements. Four bits can form 16 distinct combinations, but since only tendigits are coded, the remaining six combinations are unassignedand not used Although the minimum number of bits required to code 2ndistinct quantities is n, there is no maximum number of bitsthat may be used for a binary code.] For example, the ten decimal digits can be coded with ten bits,and each decimal digit assigned a bit combination of nine 0sand a 1.In this particular binary code, the digit 6 is assigned thebit combination Manav Rachna University Binary Codes Binary codes are codes which are represented inbinary system with modification from the originalones. Below we will be seeing the following: Weighted Binary Systems Non Weighted Codes Manav Rachna University Manav Rachna College of Engineering Weighted Binary Systems
Weighted binary codes are those which obey the positional weighting principles, each position of the number represents a specific weight. The binary counting sequence is an example Manav Rachna University Decimal 8421 2421 5211 Excess-3 0000 0011 1 0001 0100 2 0010 0101 3 0110 4 1010 0111 5 1011 1000 6 1001 7 1101 1100 8 1110 9 1111 Manav Rachna University Manav Rachna College of Engg.
Binary Codes A binary code is a group of n bits that assume up to 2n distinct combinations of 1s and 0s with each combination representing one element of the set that is being coded. Manav Rachna University Manav Rachna College of Engg. BCD Binary Coded Decimal ASCII American Standard Code for Information Interchange BCD Binary Coded Decimal
Decimal BCD Number Number When the decimal numbers are represented in BCD, each decimal digit is represented by the equivalent BCD code.(4-BITS PER DIGIT) Example :BCD Representation of Decimal 6349 Manav Rachna University 8421/BCD Codes Binary codes for decimal digits require aminimum of four bits. Numerous different codescan be obtained by arranging four or more bits inten distinct possible combinations. The BCD (Binary Coded Decimal) is a straightassignment of the binary equivalent. It ispossible to assign weights to the binary bitsaccording to their positions. The weights in theBCD code are 8,4,2,1. Example: The bit assignment 1001, can be seenby its weights to represent the decimal 9because: 1x8+0x4+0x2+1x1 = 9 Manav Rachna University When specifying data, the user likes to give the data in decimal form.
The BCD (binary-coded decimal) is a straightassigned of the binary equivalent. It is possible toassign weight to the binary bits according to theirposition. The weights in the BCD code are 8,4,2,1.The weights in the BCD code are 8,4,2,1. The bitassignment 0110 for example can be interpreted bythe weights to represent the decimal digit 6because 0X8+1X4+1X2+0X1=6. Numbers are represented in digital computerseither in binary or in decimal through a binarycode. When specifying data, the user likes to give thedata in decimal form. The input decimal numbers are stored internally inthe computer by means of decimal code. Each decimal digit requires at least four binarystorage elements. The decimal numbers are converted to binarywhen arithmetic operations are done internallywith numbers represented in binary. Manav Rachna University It is possible to perform the arithmetic operationsdirectly in decimal with all numbers left in a codedform throughout. For example, the decimal number 395, whenconverted to binary, is equal to andconsists of nine binary digits. The same number,when represented internally in the BCD code,occupies four bits of each decimal digit, for a total of12 bits The first four bits represent a3, the next four a 9 and the last four a 5. It is every important to understand the differencebetween conversion of a decimal number to binaryand the binary coding of a decimal number. In each case the final results is a series of bits. Thebits obtained from conversion are binary digits. Bits obtained from coding are combinations of 1sand 0s in the digital system may sometimesrepresent a binary number and at other timesrepresent some other discrete quantity ofinformation as specified by a given binary code. Manav Rachna University The BCD code, for example, has been chosen tobe both a code and a direct binary conversion, aslong as the decimal numbers are integers from 0to 9. For numbers greater than 9, the conversion andthe coding are completely different. This conceptis so important that it is worth repeating withanother example. The binary conversion of decimal 13 is 1101, thecoding of decimal 13 with BCD is Manav Rachna University Binary Codes for the decimal digits
(BCD) 8421 Excess-3 84-2-1 2421 (Biquinary) 0000 0011 1 0001 0100 0111 2 0010 0101 0110 3 4 5 1000 1011 6 1001 1010 1100 7 1101 8 1110 9 1111 Binary Codes for the decimal digits Manav Rachna University The components used to construct digital systems are enclosed within IC packages. It is important that the digital designer be familiar w/ the various digital components encountered in IC form BINARY CODES It is possible to assign weights to the binary bitsaccording to their positions. BCD code, , 2421, Weighted codes Numbers are represented in digital computerseither in binary or in decimal through a binarycode. Manav Rachna University When specifying data, the user likes to give the data in decimal form. 2421 Code This is a weighted code, its weights are 2, 4, 2 and 1. Adecimal number is represented in 4-bit form and thetotal four bits weight is = 9. Hence the code represents the decimal numbers from 0 to 9. Manav Rachna University 5211 Code This is a weighted code, its weights are 5, 2, 1 and 1. A decimal number is represented in 4-bit form and the total four bits weight is = 9. Hence the 5211 code represents the decimal numbers from 0 to 9. Manav Rachna University REFLECTION CODES A code is said to be reflective when code for 9 iscomplement for the code for 0, and so is for 8 and1 codes, 7 and 2, 6 and 3, 5 and 4. Codes 2421,5211, and excess-3 are reflective, whereas the code is not. Manav Rachna University Sequential Codes A code is said to be sequential when twosubsequent codes, seen as numbers in binaryrepresentation, differ by one. This greatly aidsmathematical manipulation of data. The and Excess-3 codes are sequential, whereas the and 5211 codes are not Manav Rachna University Non Weighted Codes Non weighted codes are codes that are notpositionally weighted. That is, each positionwithin the binary number is not assigned a fixedvalue. Manav Rachna University WHAT ARE GRAY CODES Manav Rachna University REFLCETED CODES Reflected Code(also known as the Gray code)
Digital systems can be designed toprocess data in discrete form only. Manyphysical systems supply continuousoutput data. These data must beconverted into digital or discrete formbefore they are applied to a digital system. Advantage: A number in the reflected codechanges by only one bit as it proceedsfrom one number to the next. Manav Rachna University Forming a Gray Code Start with all 0's
Change the least significant bit that forms a newcode word a b c d e Manav Rachna College of Engg. Binary Reflected Gray Code
Manav Rachna College of Engg. Reflected Gray and Binary Codes
Binary Gray Manav Rachna College of Engg. Why Gray Codes? Single output changes at a time
Asynchronous sampling Permits asynchronous combinational circuits to operate in fundamental mode Potential for power savings Multiphase, multifrequency clock generator Manav Rachna College of Engg. Why Gray Codes? Manav Rachna College of Engg. Why Gray Codes? Manav Rachna College of Engg. BINARY CODES Reflected Code Decimal Equivalent 0000 0001 1 0011 2 0010
0001 1 0011 2 0010 3 0110 4 0111 5 0101 6 0100 7 1100 8 Manav Rachna College of Engg. BINARY CODES 1101 9 1111 10 1110 11 1010 12 1011 13 1001 14 1000 15 Manav Rachna College of Engg. The Reflected Code Digital system can be designed to process data indiscrete form only. Many physical systems supply continuous outputdata. These data must be converted into digital ordiscrete form before they are applied to a digitalsystem. Continuous or analog information is converted touse the reflected code shown in table 1-4 torepresent the digital data converted from theanalog data. The advantage of the reflected code over purebinary numbers is that a number in the reflectedcode changes by only one bit as it proceeds fromone number to the next. A typical application of the reflected code occurswhen the analog data are represented by acontinuous change of a shaft position. The shaft is partitioned into segments, and eachsegment is assigned a number. Manav Rachna College of Engg. APPLICATION OF GRAY CODE
Manav Rachna College of Engg. APPLICATION OF GRAY CODE
Manav Rachna College of Engg. GRAY CODES Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. CONVERTING BETWEEN GRAY & BINARY CODES
Manav Rachna College of Engg. Excess-3 Code Excess-3 is a non weighted code used to expressdecimal numbers. The code derives its name fromthe fact that each binary code is thecorresponding 8421 code plus 0011(3). Example: 1000 of 8421 = 1011 in Excess-3 Manav Rachna College of Engg. EXCESS-3 CODE Manav Rachna College of Engg. Alphanumeric Codes Many applications of digital computers require thehandling of data that consist not only of numbers, butalso of letters. For instance, an insurance company with millions ofpolicy holders may use a digital computer to process itsfiles. To represent the policy holders name in binary form, itis necessary to have a binary code for the alphabet. In addition, the same binary code must representdecimal numbers and some other special characters. An alphanumeric (sometimes abbreviatedalphanumeric) code is binary code of a group of elementconsisting of special symbol such as $. The total number of elements in an in alphanumericgroup is greater than 36. Manav Rachna College of Engg. Therefore, it must be coded with a minimumofsix bits (26=64, but 25 = 32) isinsufficient.
One possible arrangement of six bitalphanumeric code is shown in Table1-5under the name internal code. With few variations, it is used in manycomputers to represent alphanumericcharacters internally. The need to represent more than 64characters (the lowercase letters and specialcontrol characters for the transmission ofdigital information) gave rise to seven andeight-bit alphanumeric codes. One such code is known as ASCII (AmericanStandard Code for InformationInterchange); another is known as EBCDIC(Extended BCD Interchange Code). Manav Rachna College of Engg. The ASCII code listed in table 1-5 consists of sevenbits but is, for all practical purposes, an eight-bitcode because an eighth bit is invariably added forparity. Most computers translate the input code into aninternal six-bit code. As an example, the internalcode representation of the name John Doe is: J O H N blank D O E Manav Rachna College of Engg. ASCII CODES The Problem
Representing text strings, such as Hello, world, in a computer Manav Rachna College of Engg. Codes and Characters Each character is coded as a byte
Most common coding system is ASCII(Pronounced ass-key) ASCII = American National Standard Code forInformation Interchange Defined in ANSI document X Manav Rachna College of Engg. ASCII Features 7-bit code 8th bit is unused (or used for a parity bit)
27 = 128 codes Two general types of codes: 95 are Graphic codes (displayable on a console) 33 are Control codes (control features of the console or communications channel) Manav Rachna College of Engg. ASCII Chart Manav Rachna College of Engg. Most significant bit Least significant bit e.g., a = 95 Graphic codes 33 Control codes Alphabetic codes Numeric codes Punctuation, etc. Hello, world Example = Binary 01001000 01100101 01101100 01101111
Hexadecimal 48 65 6C 6F 2C 20 77 67 72 64 Decimal 101 108 111 44 32 119 103 114 100 H e l o , w r d Manav Rachna College of Engg. Common Control Codes CR 0D carriage return LF 0A line feed
HT09horizontal tab DEL7Fdelete NULL00null Manav Rachna College of Engg. Hexadecimal code Terminology Learn the names of the special symbols [ ] brackets
{ }braces ( )parentheses @commercial at sign & ampersand ~tilde Manav Rachna College of Engg. Escape Sequences Extend the capability of the ASCII code set
For controlling terminals and formattingoutput Defined by ANSI in documents X and X The escape code is ESC =1B16 An escape sequence begins with twocodes:ESC [ Manav Rachna College of Engg. 5B16 1B16 Examples Erase display: ESC [ 2 J Erase line: ESC [ K
Manav Rachna College of Engg. EBCDIC Extended BCD Interchange Code (pronounced ebb-se-dick)
8-bit code Developed by IBM Rarely used today IBM mainframes only Manav Rachna College of Engg. THE END Manav Rachna College of Engg.