Binary Codes Lecture Notes PDF

Chapter3 Lecture 3: Binary Codes Objectives:  Binary codes types.  BCD code (8421 code).  Alphanumeric codes.  Excess-3 and Gray code.  Parity method for error detection. Binary codes types:  Weighted codes  BCD  6311 (8421)  2421  6...

Chapter3 Lecture 3: Binary Codes Objectives:  Binary codes types.  BCD code (8421 code).  Alphanumeric codes.  Excess-3 and Gray code.  Parity method for error detection. Binary codes types:  Weighted codes  BCD  6311 (8421)  2421  642-3  84-2-1  Non_ Weighted codes  Excess-3  Gray  Alphanumeric codes.  EBCDIC  ASCII Error detection codes (Parity). o Weighted codes and non-weighted codes are used to represent the decimal numbers. o Alphanumeric codes are used to represent the numeric and nonnumeric data (characters). o Error detection codes are used to detect the errors during the data transmission. o Weighted codes use 4 binary digits to represent (0-9) decimal numbers. 2. BCD code (8421 code)  simplest form: each decimal digit is replaced by its binary equivalent. Example1: 937.25 is represented by 937.25 1001 0011 0111 0010 0101 (937.25)= (100100110111.00100101)BCD  this representation is referred to as "Binary-Coded-Decimal": BCD or more explicitly as 8-4-2-1(8421 code). Note: The result is quite different than that obtained by converting the number as a whole into binary. Example 2: = 100001010100(BCD)  BCD is inefficient, e.g. to represent 999 and 999999 bits needed: o 10 and 20 in binary numbers o 12 and 24 for BCD code. Decimal numbers 8421(BCD) 6311 642-3 0 0000 0000 0000 1 0001 0001 0101 2 0010 0011 0010 3 0011 0100 1001 4 0100 0101 0100 5 0101 0111 1011 6 0110 1000 0110 7 0111 1001 1101 8 1000 1011 1010 9 1001 1100 1111 Example 3: convert 0110100000111001(BCD) to its decimal equivalent. Solution: Divide the BCD number into four-bit groups and convert each to decimal:  0110 1000 0011 1001 6 8 3 9 0110100000111001(BCD) = 683910  BCD is used in interfacing between a digit device and a human being, e.g. digital voltmeter (DVM). Example 4: Convert the following decimal and binary numbers to BCD. a) 564810 b) 100011012 a) 564810 =0101 0110 0100 1000 b) 100011012=14110=0001 0100 0001 Example 5: convert the BCD number 011111000001 to its decimal equivalent. 0111 1100 0001BCD = error Doesn’t exist in the BCD Code 3. Alphanumeric codes o A complete alphanumeric code would include the 26 lowercase characters, 26 uppercase characters, 10 numeric digits, etc. o There are many choices of codes sets to represent alphanumeric characters and several control characters. o Two well accepted code sets are used for information coding: EBCDIC code: extended binary coded decimal interchange code. ASCII Code: American standard code for information interchange: The ASCII code is a seven-bit code, and so it has =128 possible code groups. Example: Write the ASCII code for the message: The email is Answer: 1010100 1101000 1100101 1100101 1101101 1100001 1101001 1101100 1101001 1110011