Binary Arithmetic Operations Quiz

Study Notes

Binary Number System: A base-2 number system that uses only two digits: 0 and 1
Binary Arithmetic Operations:
- Addition: similar to decimal addition, but with carry bits (1s) and no borrow bits
- Subtraction: similar to decimal subtraction, but with borrow bits (1s) and no carry bits
- Multiplication: similar to decimal multiplication, but with binary digits
- Division: similar to decimal division, but with binary digits

Number Base Systems:
- Binary (base 2): uses 0 and 1
- Octal (base 8): uses 0-7
- Decimal (base 10): uses 0-9
- Hexadecimal (base 16): uses 0-9, A-F (A=10, B=11, ..., F=15)
Conversion Methods:
- Binary to Decimal: sum of place values (2^0, 2^1, 2^2, ...)
- Decimal to Binary: repeated division by 2 and remainder
- Hexadecimal to Decimal: sum of place values (16^0, 16^1, 16^2, ...)
- Decimal to Hexadecimal: repeated division by 16 and remainder

Use Cases:
- Color representation (RGB): #RRGGBB, where RR, GG, BB are hexadecimal values
- Memory addresses: often represented in hexadecimal format
- Data compression: hexadecimal representation can be more compact than binary
- Programming languages: hexadecimal literals are used in some languages

Signed Integer Representation:
- Most significant bit (MSB) indicates sign (0 for positive, 1 for negative)
- Remaining bits represent the magnitude
Twos Complement:
- Invert all bits (1's complement)
- Add 1 to the result
- Example: decimal -5 in 8-bit twos complement: 11111011

Bitwise AND (&):
- Bit-by-bit AND operation
- Result has 1 only if both operands have 1 in that position
Bitwise OR (|):
- Bit-by-bit OR operation
- Result has 1 if either operand has 1 in that position
Bitwise XOR (^):
- Bit-by-bit XOR operation
- Result has 1 if operands have different values in that position
Bitwise NOT (~):
- Inverts all bits (1 becomes 0, 0 becomes 1)

Binary number system uses only two digits: 0 and 1
Binary arithmetic operations have some differences compared to decimal operations:
- Addition: uses carry bits (1s) and no borrow bits
- Subtraction: uses borrow bits (1s) and no carry bits
- Multiplication: uses binary digits
- Division: uses binary digits

Number base systems include:
- Binary (base 2): uses 0 and 1
- Octal (base 8): uses 0-7
- Decimal (base 10): uses 0-9
- Hexadecimal (base 16): uses 0-9, A-F (A=10, B=11,..., F=15)
Conversion methods include:
- Binary to Decimal: sum of place values (2^0, 2^1, 2^2,...)
- Decimal to Binary: repeated division by 2 and remainder
- Hexadecimal to Decimal: sum of place values (16^0, 16^1, 16^2,...)
- Decimal to Hexadecimal: repeated division by 16 and remainder

Hexadecimal is used in various applications:
- Color representation (RGB): #RRGGBB, where RR, GG, BB are hexadecimal values
- Memory addresses: often represented in hexadecimal format
- Data compression: hexadecimal representation can be more compact than binary
- Programming languages: hexadecimal literals are used in some languages

Signed integer representation uses:
- Most significant bit (MSB) to indicate sign (0 for positive, 1 for negative)
- Remaining bits to represent the magnitude
Twos complement representation:
- Inverts all bits (1's complement)
- Adds 1 to the result
- Example: decimal -5 in 8-bit twos complement: 11111011

Bitwise AND (&) operation:
- Bit-by-bit AND operation
- Result has 1 only if both operands have 1 in that position
Bitwise OR (|) operation:
- Bit-by-bit OR operation
- Result has 1 if either operand has 1 in that position
Bitwise XOR (^) operation:
- Bit-by-bit XOR operation
- Result has 1 if operands have different values in that position
Bitwise NOT (~) operation:
- Inverts all bits (1 becomes 0, 0 becomes 1)