Topics
Number Systems
Program Analysis
Introduction to C+ +
- Introduction to C++
- Character Sets
- Standard I/O Strems in C++
- Type Modifiers
- C++ Data Types
- Variables in C++
- Constants
- Compiler Tokens
- Operators in C++
- Comments in C++
- Scope and Visibility
- Control Statements
- Functions in C++
- Default Arguments
- Techniques used to pass Variables into C++ Functions
- Function Overloading
- Inline Functions
- Recursion
- Pointers in C++
- Arrays in Data Structure
- References
- Type Conversion in Expressions
Visual Basic
Introduction to Networking and Internet
- Introduction to Networking Technology
- Networking Terms and Concepts
- Concept of Computer Network
- Network Security
- Network Applications
- Introduction Binary Addition and Subtraction
- 1’s and 2’s Complement for subtraction
Introduction to Binary Addition & Subtraction
Binary Addition:
The rules for binary addition are given in table:
| A | B | Sum | Carry | Result |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 0 |
For example,
1) (1011) + (1100)
1 0 1 1
+ 1 1 0 0
1 0 1 1 1
↑
Carry
∴ (1011)2 + (1100)2 = (10111)2
Binary Subtraction:
The rules for binary subtraction are given in table:
| A | B | Difference | Borrow |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
For example,
1) (1011)2 - (0110)2
1 0 1 1
- 0 1 1 0
1 ← borrow
0 1 0 1
∴ (1011)2 - (0110)2 = (0101)2
These rules are to be strictly followed; only then can correct results be generated.
1’s and 2’s Complement for subtraction
Subtraction using one's complement:
In a binary number, if each 1 is replaced by 0 and each 0 by 1, the resulting number is known as the one's complement of the first number.
Steps To calculate the 1's complement Subtraction
Step 1: Find binary of A
Step 2: Find 1's complement of B
Step 3: Add step 1 with step 2
Step 4: (i) If carry 1 is present, the answer is +ve make End around carry
(ii) If carry is absent answer is -ve find l's complement
Example:
1) 7 - 5:
7 0 1 1 1 0 1 1 1
- 5 - 0 1 0 1 One's Complement ⇒ + 1 0 1 0
2 Carry → 1 0 0 0 1
+ 1
0 0 1 0
Subtraction using two's complement:
If 1 is added to l's complement of a binary number, the resulting number is known as the two's complement of the binary number
Steps To calculate the 2's complement Subtraction
Step 1: Find binary of A
Step 2: Find 2's complement of B
Step 3: Add step 1 with step 2
Step 4: (i) If carry 1 is present answer is +ve Delete the carry
(ii) If carry is absent answer is -ve find 2's complement
Example:
1) 7 - 5:
7 0 1 1 1 0 1 1 1
- 5 - 0 1 0 1 \[\ce{->[two's complement]}\] + 1 0 1 1
2 1 0 0 1 0
↑
discard carry
The answer is (0010)2
