Page 1 Chapter 1 19 ARITHMETIC OPERATIONS - Binary Arithmetic § Single Bit Addition with Carry § Multiple Bit Addition § Single Bit Subtraction with Borrow § Multiple Bit Subtraction § Multiplication § BCD Addition Page 2 Chapter 1 19 ARITHMETIC OPERATIONS - Binary Arithmetic § Single Bit Addition with Carry § Multiple Bit Addition § Single Bit Subtraction with Borrow § Multiple Bit Subtraction § Multiplication § BCD Addition Chapter 1 20 Single Bit Binary Addition with Carry Given two binary digits (X,Y), a carry in (Z) we get the following sum (S) and carry (C): Carry in (Z) of 0: Carry in (Z) of 1: Z 1 1 1 1 X 0 0 1 1 + Y + 0 + 1 + 0 + 1 C S 0 1 1 0 1 0 1 1 Z 0 0 0 0 X 0 0 1 1 + Y + 0 + 1 + 0 + 1 C S 0 0 0 1 0 1 1 0 Page 3 Chapter 1 19 ARITHMETIC OPERATIONS - Binary Arithmetic § Single Bit Addition with Carry § Multiple Bit Addition § Single Bit Subtraction with Borrow § Multiple Bit Subtraction § Multiplication § BCD Addition Chapter 1 20 Single Bit Binary Addition with Carry Given two binary digits (X,Y), a carry in (Z) we get the following sum (S) and carry (C): Carry in (Z) of 0: Carry in (Z) of 1: Z 1 1 1 1 X 0 0 1 1 + Y + 0 + 1 + 0 + 1 C S 0 1 1 0 1 0 1 1 Z 0 0 0 0 X 0 0 1 1 + Y + 0 + 1 + 0 + 1 C S 0 0 0 1 0 1 1 0 Chapter 1 21 § Extending this to two multiple bit examples: Carries 0 0 Augend 01100 10110 Addend +10001 +10111 Sum § Note: The 0 is the default Carry-In to the least significant bit. Multiple Bit Binary Addition Page 4 Chapter 1 19 ARITHMETIC OPERATIONS - Binary Arithmetic § Single Bit Addition with Carry § Multiple Bit Addition § Single Bit Subtraction with Borrow § Multiple Bit Subtraction § Multiplication § BCD Addition Chapter 1 20 Single Bit Binary Addition with Carry Given two binary digits (X,Y), a carry in (Z) we get the following sum (S) and carry (C): Carry in (Z) of 0: Carry in (Z) of 1: Z 1 1 1 1 X 0 0 1 1 + Y + 0 + 1 + 0 + 1 C S 0 1 1 0 1 0 1 1 Z 0 0 0 0 X 0 0 1 1 + Y + 0 + 1 + 0 + 1 C S 0 0 0 1 0 1 1 0 Chapter 1 21 § Extending this to two multiple bit examples: Carries 0 0 Augend 01100 10110 Addend +10001 +10111 Sum § Note: The 0 is the default Carry-In to the least significant bit. Multiple Bit Binary Addition Chapter 1 22 § Given two binary digits (X,Y), a borrow in (Z) we get the following difference (S) and borrow (B): § Borrow in (Z) of 0: § Borrow in (Z) of 1: Single Bit Binary Subtraction with Borrow Z 1 1 1 1 X 0 0 1 1 -Y -0 -1 -0 -1 BS 11 1 0 0 0 1 1 Z 0 0 0 0 X 0 0 1 1 -Y -0 -1 -0 -1 BS 0 0 1 1 0 1 0 0 Page 5 Chapter 1 19 ARITHMETIC OPERATIONS - Binary Arithmetic § Single Bit Addition with Carry § Multiple Bit Addition § Single Bit Subtraction with Borrow § Multiple Bit Subtraction § Multiplication § BCD Addition Chapter 1 20 Single Bit Binary Addition with Carry Given two binary digits (X,Y), a carry in (Z) we get the following sum (S) and carry (C): Carry in (Z) of 0: Carry in (Z) of 1: Z 1 1 1 1 X 0 0 1 1 + Y + 0 + 1 + 0 + 1 C S 0 1 1 0 1 0 1 1 Z 0 0 0 0 X 0 0 1 1 + Y + 0 + 1 + 0 + 1 C S 0 0 0 1 0 1 1 0 Chapter 1 21 § Extending this to two multiple bit examples: Carries 0 0 Augend 01100 10110 Addend +10001 +10111 Sum § Note: The 0 is the default Carry-In to the least significant bit. Multiple Bit Binary Addition Chapter 1 22 § Given two binary digits (X,Y), a borrow in (Z) we get the following difference (S) and borrow (B): § Borrow in (Z) of 0: § Borrow in (Z) of 1: Single Bit Binary Subtraction with Borrow Z 1 1 1 1 X 0 0 1 1 -Y -0 -1 -0 -1 BS 11 1 0 0 0 1 1 Z 0 0 0 0 X 0 0 1 1 -Y -0 -1 -0 -1 BS 0 0 1 1 0 1 0 0 Chapter 1 23 § Extending this to two multiple bit examples: Borrows 0 0 Minuend 10110 10110 Subtrahend - 10010 - 10011 Difference § Notes: The 0 is a Borrow-In to the least significant bit. If the Subtrahend > the Minuend, interchange and append a – to the result. Multiple Bit Binary SubtractionRead More

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