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Chapter 1 - PPT - Mano & Kime - 3rd EdSlide 1 Lecture 3 Binary ArithmeticLecture 3 Binary Arithmetic
Slide 2 OutlineOutline Single Bit Addition with Carry Multiple Bit Addition Single Bit Subtraction with Borrow Multiple Bit Subtraction Multiplication
Slide 3 Single Bit Binary Addition with CarrySingle Bit Binary Addition with Carry
Slide 4 Multiple Bit Binary AdditionExtending this to a multiple bit examples: Multiple Bit Binary Addition 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 Carries Augend Addend Sum 0 0 1 1
Carries 00000 01100 Augend 01100 10110 Addend +10001 +10111 Sum 11101 101101
Slide 5 Multiple Bit Binary AdditionExtending this to a multiple bit examples: Multiple Bit Binary Addition 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 Carries Augend Addend Sum 0 0 1 1 1
Carries 00000 01100 Augend 01100 10110 Addend +10001 +10111 Sum 11101 101101
Slide 6 Single Bit Binary Subtraction with BorrowGiven 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
Slide 7 Multiple Bit Binary SubtractionExtending this to a multiple bit example: 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 Subtraction 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 Borrows Minuend Subtrahend Difference 0 0 0 0
Borrows 00000 00110 Minuend 10110 10110 Subtrahend 10010 10011 Difference 00100 00011
Slide 8 Multiple Bit Binary SubtractionExtending this to a multiple bit examples: 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 Subtraction 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 Borrows Minuend Subtrahend Difference 0 0 1 1
Borrows 00000 00110 Minuend 10110 10110 Subtrahend 10010 10011 Difference 00100 00011
Slide 9 Binary MultiplicationBinary Multiplication
Slide 10 SummarySummary Single Bit Addition with Carry Multiple Bit Addition Single Bit Subtraction with Borrow Multiple Bit Subtraction Multiplication
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