Download EECC201 Freshman Seminar Intro to Micro controller Dr. Ken …

EECC201 Freshman Seminar
Intro to Micro controller
Dr. Ken Hsu
WEEK 7
ADDITION, SUBTRACTION AND
COMPARE OF BINARY
NUMBERS
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Binary numbers
Unsigned decimal
Signed Decimal
Hexadecimal
0000
0
0
0
0001
1
1
1
0010
2
2
2
0011
3
3
3
0100
4
4
4
0101
5
5
5
0110
6
6
6
0111
7
7
7
1000
8
-8
8
1001
9
-7
9
1010
10
-6
A
1011
11
-5
B
1100
12
-4
C
1101
13
-3
D
1110
14
-2
E
1111
15
-1
F
2’S COMPLEMENT
0100
+10111
1100
Take 1’s complement
Add 1 to result
Get 2’s complement
To distinguish between two numbers with the same sign and two
numbers with different signs in assembly language programming
AND
Num1,#80H
AND
Num2,#80H
XOR
Num1,Num2
If result of XOR = 0 then Z flag is set to 1 and sign of
both numbers is the same
If result of XOR = 1 then Z flag is set to 0 and sign of
the numbers are different.
NOTE: 80H is called a MASK.
ADDITION
Unsigned number addition
(1) Numbers with same sign
(a) Positive
c Carry 1 bit
1 XOR 1 = No overflow
1111
1111
15
1011
11
11010
26
+
CY flag set to 1
This means that more than 4 bit
is needed to represent sum.
ADDITION
Signed number addition
(1) Numbers with same sign
(a) Negative
1 XOR 1 = No overflow
1111
1111
-1
1011
-5
11010
-6
+
CY flag set to 1
Ignore carry since there is
no overflow
ADDITION
Signed number addition
(1) Numbers with different sign
1000
+
0111
-8
01111
-1
+7
CY flag set to 0
SUBTRACTION
(COMPARE CMP)
Unsigned number subtraction
(1) Numbers with different sign
-
0 XOR 1 = overflow
0011
+3
1011
-5
Do 2’s Complement with
second number and add
with first number
01
0011
+
0101
01000
8
Carry is 0. Make sign bit
positive and thus equal to 8
and not -8.
SUBTRACTION
(COMPARE CMP)
Unsigned number subtraction
(1) Numbers with same sign
(a) Positive
-
1111
15
1011
11
Do 2’s Complement with
second number and add
with first number
1 XOR 1 = No overflow
1111
1111
+
0101
10100
4
Ignore carry since there is
no overflow
SUBTRACTION
(COMPARE CMP)
Unsigned number subtraction
(1) Numbers with same sign
(a) Negative
-
1111
-1
1011
-5
Do 2’s Complement with
second number and add
with first number
1 XOR 1 = No overflow
1111
1111
+
0101
10100
4
Ignore CY since there is no
overflow
SUBTRACTION
(COMPARE CMP)
Unsigned number subtraction
(1) Numbers with different sign
-
1 XOR 0 = overflow
1000
-8
0111
+7
Do 2’s Complement with
second number and add
with first number
10
1000
+
1001
10001
Overflow. This means that
-15 more than 4 bit is needed to
represent number.
AVERAGE OF 2 NUMBERS
NOTE: If the average of a positive number gives a
fraction, round fraction down.
(1) Average of a positive number with a whole result
1111
1111 15
+
1011 11
11010 26
Rotate right with carry
by 1 bit.
01101 13
RORC
AVERAGE OF 2 NUMBERS
NOTE: If the average of a positive number gives a
fraction, round fraction down.
(1) Average of a positive number with a fractional result.
+
1000 8
0111
7
01111 15
0111 7.5
7
Rotate right with carry
by 1 bit.
RORC
AVERAGE OF 2 NUMBERS
NOTE: If the average of a negative number gives a
fraction, round fraction down.
(1) Average of a negative number with a whole result.
1111
1111 -1
+
1011 -5
11010
-6
Rotate right with carry
by 1 bit.
01101
-3
RORC
AVERAGE OF 2 NUMBERS
NOTE: If the average of a negative number gives a
fraction, round fraction down.
(1) Average of a negative number with a fractional result.
1000 -8
+
0111 +7
01111
-1
NOT1 CY
11111
11111
-0.5
Rotate Right with carry
by 1 bit.
RORC
-1