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Introduction, Number systems
and Conversion (B)
Hasan Zidan
Department of Electrical Engineering
AUST
1
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View Full Document Binary Arithmetic
The rules for binary (
+
)
rithmetic are:
The rules for binary (

)
btraction are:
arithmetic are:
0
+
0 =
0,
carry
= 0
subtraction are:
0

0 =
0,
borrow
= 0
1
+
0 =
1,
carry
= 0
rry
1

0 =
1,
borrow
= 0
orrow
0
+
1 =
1,
carry
= 0
1
+
1 =
0,
carry
= 1
0

1 =
1,
borrow
= 1
1

1 =
0,
borrow
= 0
Carries,
Borrows
to
/
from
left of current digit.
Binary
addition
,
subtraction
works the same as
decimal addition,
2
subtraction
.
Binary, Decimal Addition
Decimal
1
0
1
0
1
1
Binary
1
1
3
4
+ 1
7

+
0
0
0
0
0
1

5
1
From LSD to MSD:
carry
next
1
0
1
1
0
0
From LSB to MSB:
=
carry
7+4
= 1
;
carry
1
to next
column
1
(carry) + 3 + 1 = 5.
1+1
0
, carry
1
1 (carry)+1+0 = 0
, carry
1
1 (carry)+0 + 0 = 1
, no carry
answer =
5
1
.
1 +0
= 1
0 + 0 = 0
1 + 0 = 1
3
answer =
1
0
1
1
0
0
2
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View Full Document Subtraction
Decimal
Binary
91
0
0
9
0
0

0
0
1
1
0
0
0
0
1
10
1

8
9
9

0
1
1
01
= 9
;
borrow 1 from
next column
0 1 (borrow)0=
9
,
01
= 1
;
borrow
1
from
next column
orrow)
()
,
borrow 1
9
 1 (borrow) 
0
=
8
.
nswer =
0 1 (borrow)  0 = 1
,
borrow 1
1  1 (borrow)  0 = 0.
4
Answer =
8
9
9
.
Answer
=
0
1
1
.
Binary Multiplication
The rules for binary (
*
)
rithmetic are:
0
*
0 =
0
arithmetic are:
1 1 0 1

1 1 0 1
*
1
0
1
1
(multiplicand)
(multiplier)
1
*
0 =
0
1 1 0 1
0 0 0 0
1 1 0 1
0
*
1 =
0
*
=

1 0 0 0 1 1 1 1
2
= 143
10
(
Product
)
1
1
1
5
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View Full Document Binary Division
1 0 0 1 0
0
0
1
1 0 1 1
1
1
0
1
(dividend)
(divisor)
(quotient)
1 0 1 1
1 1 1
0
011
()
1 0 1 1
1 1
0
1
1 0 1 1
artial remainder)
1 0
(partial remainder)
6
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This note was uploaded on 03/10/2012 for the course ENGINEERIN 131231 taught by Professor Dr.hamad during the Spring '12 term at Amity University.
 Spring '12
 Dr.Hamad
 Electrical Engineering

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