BINARY ARITHMETIC AND TWO's COMPLEMENT ARITHMETIC

30 Pages·2007·0.04 MB·English

CChhaapptteerr 33
BINARY ARITHMETIC AND
TWO’s COMPLEMENT
ARITHMETIC
Lesson 3
BINARY MULTIPLICATION
AND DIVISION
Ch03L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 2
2006
Outline
(cid:127)(cid:127) MMuullttiipplliiccaattiioonn: Unsigned Numbers
(cid:127)(cid:127) MMuullttiipplliiccaattiioonn: Signed Numbers
(cid:127) Division
Ch03L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 3
2006
××××
Multiplication of 1-bit 1-bit
(cid:127) Dot operator represents an AND
operation. AND operations.
(cid:127) 1. 1 = 1 …..(1)
(cid:127) 1. 0 = 0 …..(2)
(cid:127) 0. 1 = 0 …..(3)
(cid:127) 0. 0 = 0 …..(4)
Ch03L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 4
2006
××××
Multiplication of n-bit 1-bit
(cid:127) Perform AND operation on all n-bits
with the multiplying bit
(cid:127) Multiplication by 1 gives same
b
number as before
Example 1: 1 0 1 1
××××
1
Using Equations (1) and (2)
Answer is 1 0 1 1
Ch03L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 5
2006
××××
Multiplication of n-bit 1-bit
Multiplication by 0 gives all 0s.
b
Example 2: 1 0 1 1
××××
0
Using Equations (1) and (2)
Answer is 0 0 0 0
Ch03L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 6
2006
Shift left operation by 1-bit
Example 3: 1 0 1 1
Shift Left
Answer is 0110.
(Place of each bit moves to left and msb
is discarded.)
Ch03L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 7
2006
Shift left operation by 2-bit
Example 3: 1 0 1 1
Shift Left Twice
Answer is shift once 0110. Shift again
1100
Ch03L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 8
2006
××××
Multiplication of n-bit m-bit

Step1: Find P0 Multiple n-bit by rightmost
1-bit

Steps 2 and 3: Find P1 Multiple n-bit by
rightmost but 1-bit and shift left once and
add with P0 and find S0

Steps 4 and 5: Find P2 Multiple n-bit by
rightmost but 2-bits and shift left 2 times,
add by S0. and find S1
Ch03L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 9
2006
××××
Multiplication of n-bit m-bit
Continue till all m-bits are multiplied
and sum of partial products P0 + P1 + P is
m-1
found
Ch03L3-"Digital Principles and Design", Raj Kamal, Pearson Education, 10
2006