compliment representation and code ascii

numerical on 1s compliment and 2s compliment

1. 1’s and 2’s complement

2. Binary number system is the type of most popular Number Representation techniques  that used in digital systems. In the Binary System, there are only two symbols or possible digit values, i.e., 0 (off) and 1 (on). Represented by any device that only 2 operating states or possible conditions.

3. 1’s complement 1’s complement of a given binary number is obtained by replacing 1 instead of 0 and 0 instead of 1 Find out 1’s complement of binary number 101101 1’s complement is 010010 111001 1’s complement is 000110 01010110 1’s complement is 10101001

4. Example-1:   Find 1’s complement of binary number 10101110. Example-2 :   Find 1’s complement of binary number 10001.001. Example-3 :   Find 1’s complement of each 3 bit binary number.

5. 2’s complement 2’s complement of a given binary number is obtained by adding1 to 1’s complement Find out 2’s complement of binary number 101101 1’s complement is 010010 2’s complement is 010010+1=010011 111001 1’s complement is 000110 2’s complement is 000110+1=000111 01010110 1’s complement is 10101001 2’s comp.. is 10101001+1=10101010

6. 5.0 Binary-Coded-Decimal (BCD) Conversions between decimal and binary can become long and complicated for large numbers. For example, convert 874 10 to binary. The answer is 1101101010 2 , but it takes quite a lot of time and effort to make this conversion. We call this straight binary coding.

7. 5.1 Binary-Coded-Decimal (BCD) The Binary-Coded-Decimal (BCD) code makes conversion much easier. Each decimal digit, 0 through 9, is represented with a 4-Bit BCD code as shown below. The BCD code 1010, 1011, 1100, 1101, 1110 and 1111 are not used.

8. Conversion between BCD and decimal is accomplished by replacing a 4-bit BCD for each decimal digit. For example, 874 10 = 1000 0111 0100 BCD . BCD is not another number system like binary, octal, decimal and hexadecimal. It is in fact the decimal system with each digit encoded in its binary equivalent. A BCD code is not the same as a straight binary number. For example, the BCD code requires 12 bits, while the straight binary number requires only 10 bits to represent 873 10 . 5.2 Decimal  BCD Conversion

9. A BCD code is converted into a decimal number by taking groups of 4 bits, starting from LSB, and replacing them with a BCD code. For example, 1 1001 0111 1000 BCD = 1978 10 5.3 BCD  Decimal Conversion

10. BCD ADDITION:- Addition of BCD (8421) is performed by adding two digits of binary, starting from least significant digit. In case if the result is an illegal code (greater than 9) or if there is a carry out of one then add 0110(6) and add the resulting carry to the next most significant.

11. BCD SUBTRACTION:- The BCD subtraction is performed by subtracting the digits of each 4 – bit group of the subtrahend from corresponding 4 – bit group of the minuend in the binary starting from the LSD. If there is no borrow from the next higher group then no correction is required. If there is a borrow from the next group, then 6 (0110) is subtracted from the difference term of this group. For example:- Subtract 147.8 from 206.7 using 8421 BCD code.