PPT: Binary Arithmetic | Digital Electronics - Electrical Engineering (EE) PDF Download

 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 Subtraction