Binary Arithmetic Operations Quiz

Binary Arithmetic

• 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 Conversion

• 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

Hexadecimal Applications

• 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

Twos Complement Representation

• 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 Operations

• 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 Arithmetic

• 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 Conversion

• 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 Applications

• 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

Twos Complement Representation

• 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 Operations

• 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)