Binary Arithmetic
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Binary Arithmetic Operations, Summaries of Communications Law
A comprehensive overview of the fundamental binary arithmetic operations, including addition, subtraction, multiplication, and division. It explains the step-by-step process for each operation, highlighting the key concepts and rules that govern binary arithmetic. The alignment of operands, handling of carries and borrows, and the application of basic binary multiplication and division rules. It also includes illustrative examples to demonstrate the practical implementation of these binary arithmetic techniques. This resource is valuable for students and professionals who need to understand and apply binary arithmetic in various computing and engineering domains.
Typology: Summaries
2023/2024
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Binary Arithmetic
BINARY ADDITION
The two numbers (or terms) to be added are aligned at the radix point and addition begins at the least significant bit. If the sum of the least significant position yields a value with two bits (e.g., 10 2 ), then the least significant bit is recorded, and the most significant bit is carried to the next higher position. The sum of the next higher position is then performed including the potential carry bit from the prior addition. This process continues from the least significant position to the most significant position.
BINARY SUBTRACTION
In subtraction, the formal terms for the two numbers being operated on are minuend and subtrahend. The subtrahend is subtracted from the minuend to find the difference. In longhand subtraction, the minuend is the top number, and the subtrahend is the bottom number. For a given position if the minuend is less than the subtrahend, it needs to borrow from the next higher order position to produce a difference that is positive. If the next higher position does not have a value that can be borrowed from (i.e., 0), then it in turn needs to borrow from the next higher position and so forth.
BINARY SUBTRACTION
- . 1
0 10
BORROW REQUIRED
1 0
(^010)
BORROW REQUIRED
(^01)
BINARY MULTIPLICATION
In Binary Multiplication it is important to understand four basic rules in Binary Multiplication
0 x 0= 0 0 x 1= 0 1 x 0 = 1 x 1 = 1
BINARY MULTIPLICATION
What is the product 10.11 2 and 10.1 2?
1 0. 1 1
1 0. 1
x __________
1 0 1 1
0 0 0 0
1 0 1 1
Binary Multiplication is just the same as decimal multiplication
Apply the rules of Binary Addition. Apply placeholders zeroes.
1 10. 1 1 1
BINARY DIVISION
Division in the binary number system is just the same procedure as division in the decimal system
(^10) 1011.
- (^10)
Apply the rule in Binary Subtraction
011
10
10 10
This will resort to zero and this means were done