Multiple – Precision Binary Numbers
- Single – precision
- One – byte unsigned (range: 0 – 225)
- Double – precision
- Two – byte unsigned (range: 0 – 65 535)
- Triple – precision
- Three – byte unsigned (range: 0 – 16 777 215)
Addition
When adding binary numbers, the microprocessor produces two types of information:
- the sum of the two numbers (answer);
- information indicating whether there where carries in a certain columns.
*The five binary addition combination
1 1
1) 0 2) 0 3) 1 4) 1 5) 1
+ 0 + 1 + 0 + 1 1
0 1 1 10 + 1
11
1 1
1) 0 2) 0 3) 1 4) 1 5) 1
+ 0 + 1 + 0 + 1 1
0 1 1 10 + 1
11
Addition with carry
The carry from the 8th bit to the 9th bit can be used during multiple- precision arithmetic. We use the multiple – precision arithmetic when the accumulator cannot accept numbers large enough for the desired operation.
Subtraction
When subtracting binary numbers, the microprocessor produces two types of information:
- the difference between two numbers (answer);
- whether there were borrows in certain columns.
*The four binary subtraction numbers
1
1) 0 2) 1 3) 1 4) 0
- 0 - 0 - 1 - 1
0 1 0 1
Subtraction with carry
Tells us that the produce answer (difference) of the microprocessor had to borrow a 1 from a 9th bit. This occurs when the top number (minuend) is smaller than the bottom number (subtrahend).
Sir, if there's addition and subtraction of binary, is there multiplication and division? And how to solve it?
ReplyDeleteYes it has multiplication and division. In solving those two operations, they are rules to follow.
DeleteMultiplication:
0 x 0 = 0
0 x 1 = 0
1 x 0 = 0
1 x 1 = 1, and no carry or borrow bits
For example,
00101001 × 00000110 = 11110110; (41x6=246)
Binary multiplication is the same as repeated binary addition; add the multicand to itself the multiplier number of times. The rules of binary multiplication are the same as the truths of the AND gate.
Division:
Binary division is the repeated process of subtraction, just as in decimal division.
For example,
00101010 ÷ 00000110 = 00000111 (42/6=7)
This rules helps you to multiply and divide binary numbers. For more information you can see this site: http://academic.evergreen.edu/projects/biophysics/technotes/misc/bin_math.htm
Thank you Sir.
Delete:D
DeleteSir ck, where can we apply this in real life?
ReplyDeleteHi Jen!
DeleteArithmetic sequences, like many mathematical equations, require a basic set-up to allow problem-solving to begin. The first step in working towards a solution requires analyzing the situation to produce basic, preliminary information. When trying to find the maximum seating capacity of an auditorium, for instance, the process begins with determining the maximum number of seats that can be occupied in each row. Working row by row to count seats is a form of simple addition, performed in a series that leads to a total number of seats.
Once the total is identified, the next step involves determining whether the problem is inherently algebraic or geometric, which then determines the proper formula to use. That is accomplished by looking for patterns, such as a set number of added seats per row.