Binary representation and manipulation
GOOD DAY, students. This is lesson 11 in our series. In this week’s lesson, I will continue to look at binary representation and manipulation.
FINDING THE ONES COMPLEMENT OF AN INTEGER NUMBER
The ones complement representation simply involves flipping the bits of a given number. You flip zeros to ones and ones to zeros. Ensure the number is in its positive form, whether four or eight bits, before you find the ones complement of the number.
FINDING THE TWOS COMPLEMENT OF AN INTEGER NUMBER
This is another method of representing integers. This enables subtraction to be performed by a modified form of addition, which is easier to execute in the computer.
If the number is positive or negative, do the following:
Step 1: Write the number in its positive sign and magnitude form. Step 2: Flip the bits (find its one complement). Step 3: Add one (1) to the number obtained in step 2. Step 4: The result is the number in its two’s complement notation. Step 4: -17 = 11101111 (twos compliment notation)
CONVERTING A TWOS COMPLEMENT INTEGER TO DECIMAL
To carry out this conversion, you would apply the same concept you learnt in lesson 8, in terms of converting binary numbers into decimal.
Let us use the twos complement value of -17 we obtained above to be converted to decimal.
CODING SCHEMES ASSOCIATED WITH DATA REPRESENTATION
The combinations of 0s and 1s used to represent characters are defined by patterns, called a coding scheme. Using one type of coding scheme, the number one is represented as 00110001. Two popular coding schemes are American Standard Code for Information Interchange (ASCII) and Extended Binary Coded Decimal Interchange Code (EBCDIC). ASCII is used mainly on personal computers, while EBCDIC is used primarily on mainframe computers. 3. Add the binary equivalent of 2 to the ASCII representation of ‘h’ as shown below.
Here are the answers to the practice questions you were given in the previous lesson on BCD. Did you complete the questions correctly? If you did, keep up the good work. 1. (a) 8978 = 1000100101111000 or 10101000100101111000 (b) -62 = 101101100010 (c) 4560 = 0100010101100000 2. (a) 0001/0101/1000 = 158 (b) 1011/0111/0000/0101 = - 305
We have come to the end of this lesson. See you next week, when we will continue to look at binary representation and manipulation. Remember, if you fail to prepare, you prepare to fail.