Code conversion r006
- 1. Codes Computers and digital circuits processes information in the binary format. Each character is assigned 7 or 8 bit binary code to indicate its character which may be numeric, alphabet or special symbol. Example - Binary number 1000001 represents 65(decimal) in straight binary code, alphabet A in ASCII code and 41(decimal) in BCD code.
- 2. Types of codes • BCD (Binary-Coded Decimal) code : • ASCII (American Standard Code Information Interchange) code : • EBCDIC (Extended Binary Coded Decimal Interchange Code) code • Gray code • Excess-3 code
- 3. BCD (Binary-Coded Decimal) code : • Four-bit code that represents one of the ten decimal digits from 0 to 9. • Example - (37)10 is represented as 0011 0111 using BCD code, rather than (100101)2 in straight binary code. • Thus BCD code requires more bits than straight binary code. • Still it is suitable for input and output operations in digital systems. • Note: 1010, 1011, 1100, 1101, 1110, and 1111 are INVALID CODE in BCD code.
- 4. ASCII (American Standard Code Information Interchange) code : • It is 7-bit or 8-bit alphanumeric code. • 7-bit code is standard ASCII supports 127 characters. • Standard ASCII series starts from 00h to 7Fh, where 00h-1Fh are used as control characters and 20h-7Fh as graphics symbols. • 8-bit code is extended ASCII supports 256 symbols where special graphics and math's symbols are added. • Extended ASCII series starts from 80h to FFh.
- 5. EBCDIC (Extended Binary Coded Decimal Interchange Code) code • 8-bit alphanumeric code developed by IBM, supports 256 symbols. • It was mainly used in IBM mainframe computers. Gray code • Differs from leading and following number by a single bit. • Gray code for 2 is 0011 and for 3 is 0010. • No weights are assigned to the bit positions. • Extensively used in shaft encoders.
- 6. Excess-3 code • 4-bit code is obtained by adding binary 0011 to the natural BCD code of the digit. • Example - decimal 2 is coded as 0010 + 0011 = 0101 as Excess-3 code. • It not weighted code. • Its self-complimenting code, means 1's complement of the coded number yields 9's complement of the number itself. • Used in digital system for performing subtraction operations.
- 7. There are many methods or techniques which can be used to convert code from one format to another. We'll demonstrate here the following • Binary to BCD Conversion • BCD to Binary Conversion • BCD to Excess-3 • Excess-3 to BCD Binary to BCD Conversion Steps Step 1 -- Convert the binary number to decimal. Step 2 -- Convert decimal number to BCD. Example − convert (11101)2 to BCD.
- 8. Step 1 − Convert to Decimal Binary Number − 111012 Calculating Decimal Equivalent − Step Binary Number Decimal Number Step 1 111012 ((1 × 24) + (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20))10 Step 2 111012 (16 + 8 + 4 + 0 + 1)10 Step 3 111012 2910 Binary Number − 111012 = Decimal Number − 2910 Step 2 − Convert to BCD Decimal Number − 2910 Calculating BCD Equivalent. Convert each digit into groups of four binary digits equivalent. Step Decimal Number Conversion Step 1 2910 00102 10012 Step 2 2910 00101001BCD Result (11101)2 = (00101001)BCD
- 9. BCD to Binary Conversion Steps Step 1 -- Convert the BCD number to decimal. Step 2 -- Convert decimal to binary. Example − convert (00101001)BCD to Binary. Step 1 - Convert to BCD BCD Number − (00101001)BCD Calculating Decimal Equivalent. Convert each four digit into a group and get decimal equivalent for each group. Step BCD Number Conversion Step 1 (00101001)BCD 00102 10012 Step 2 (00101001)BCD 210 910 Step 3 (00101001)BCD 2910 BCD Number − (00101001)BCD = Decimal Number − 2910
- 10. Step 2 - Convert to Binary • Used long division method for decimal to binary conversion. • Decimal Number − 2910 • Calculating Binary Equivalent − Step Operation Result Remainder Step 1 29 / 2 14 1 Step 2 14 / 2 7 0 Step 3 7 / 2 3 1 Step 4 3 / 2 1 1 Step 5 1 / 2 0 1 Decimal Number − 2910 = Binary Number − 111012 Result (00101001)BCD = (11101)2
- 11. Result (1001)BCD = (1100)XS-3 BCD to Excess-3 Steps Step 1 -- Convert BCD to decimal. Step 2 -- Add (3)10 to this decimal number. Step 3 -- Convert into binary to get excess-3 code. Example − convert (1001)BCD to Excess-3. Step 1 − Convert to decimal (1001)BCD = 910 Step 2 − Add 3 to decimal (9)10 + (3)10 = (12)10 Step 3 − Convert to Excess-3 (12)10 = (1100)XE-3
- 12. Excess-3 to BCD Conversion Steps Step 1 -- Subtract (0011)2 from each 4 bit of excess-3 digit to obtain the corresponding BCD code. Example − convert (10011010)XS-3 to BCD. Given XE-3 number = 10011010 Subtract (0011)2 = 00110011 _______________ BCD 01100111 RESULT : (10011010)Xe-3 =(01100111)BCD