Department of Electrical Engineering

University of Arkansas

ELEG3923 Microprocessor
Ch.6 Arithmetic and Logics
Dr Jingxian Wu
Dr.
wuj@uark.edu
 2

OUTLINE

• Arithmetic instructions

• Signed number operations

• Logic and compare instructions

• Rotate instruction and data serialization

• BCD, ASCII
 3

AROTHMETIC: ADDC
• ADDC (add with carry)
– ADDC A, source
– (A) = (A) + source + CY
– Destination must be register A!
– Example: write a program to find the sum of 3CE7H and 3B8DH. Save the
lower byte in R6, the higher byte in R7.
CLR C
MOV A, #0E7H
ADD A, #8DH ; the sum of lower byte
MOV R6, A ; lower byte in R6

MOV A, #3CH
ADDC A, #3BH ; the sum of higher byte,
; consider the carry from lower byte
MOV R7, A
 4

ARITHMETIC: BCD
• Binary coded decimal (BCD)
– Use 4-bit binary codes to represent decimal numbers. Totally 10 codes
corresponding to decimal number 0 – 9.
– Difference
Diff from
f binary
bi number
b or hex
h number:
b
• BCD contains only 10 codes
• Any binary number larger than 9 (e.g. 1010) is not a BCD code.
• Unpacked BCD
– Use a single byte (8 bits) to represent 1 BCD code (4 bits)
– The high 4 bits are zeros, and low 4 bits are BCD. E.g. (00001000)
– Convenient to store BCD in 8-bit registers.
– E.g. unpacked BCD representation of decimal number 17: 0000 0001, 0000 0111
• Packed BCD
– A single byte (8 bits) is used to represent 2 BCD codes.
– E.g. packed BCD representation of decimal number 17: 0001 0111
– A binary sequence can be used to represent either BCD or HEX.
• E.g. 0001 0111 (BCD: 17 decimal) (HEX: 17H)
• The programmer must know which code (BCD or HEX) is actually used.
 5

ARITHMETIC: BCD ADDTION

• Addition of BCD numbers
– Advantage of packed BCD: easy to use and read
• E.g. Packed BCD of 39 decimal is 0011 1001
– Disadvantage: the ADD instruction cannot be used for BCD numbers
• E.g. 1. find 17+28 by using BCD
MOV A, #17H
ADD A, #28H
– The result is 3F, the high 4-bit is BCD, the low 4-bit is not BCD.
– To make it a BCD, add 6 to the low 4-bit: 3FH + 06H = 45H, which
is the packed BCD for 45 decimal.
• E.g. 2. find 52+87 by using BCD
MOV A, #52H
ADD A, #87H
– The result is D9, the high 4-bit is BCD, the low 4-bit is not BCD
– To make it a BCD, add 6 to the high 4 bit: D9H+60H = 139H
– After summation, if 4-bit is not BCD, add 6 to it to adjust it to BCD.
• This can be done automatically!
 6

ARITHMETIC: DA
• DA (decimal adjust for addition)
– Convert the sum of 2 BCD numbers to a BCD number
– E.g. (demo)
MOV A, #47H
ADD A, #25H ; (A) = 6CH
DA A ; adjust for BCD addition, (A) = 72H
– Operation of DA
• If lower nibble is not BCD, or if AC = 1, add 0110 to lower nibble
• If higher nibble is not BCD, or if CY = 1, add 0110 to lower nibble
– Notes:
• Can only be used for register A
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ARITHMETIC: UNSIGNED NUMBER SUBTRACTION

• SUBB (subtraction with borrow)

– SUBB A, source ; (A) = (A) – source – CY
– Example: find 3FH – 23H
CLR C ; (CY) = 0
MOV A, #3FH
SUBB A, #23H

– For two unsigned numbers A and B, A – B = A + (2’s complement of B)

– Operations of SUBB
• 1. Find the 2’s complement of source
• 2. find the summation of A and 2’s complement of source
• 3. Invert the carry
 8

ARITHMETIC: UNSIGNED NUMBER SUBTRACTION

• SUBB (Cont’d)
(C t’d)
– Example: find 4CH – 6EH
CLR C
MOV A,
A #4CH
SUBB A, #6EH

– If CY = 0 after SUBB, the result is positive;

– If CY = 1 after SUBB, the result is negative, and reg. A contains the absolute
value of the result in the form of 2’s complement
p
– Find the decimal value of the result in the above example
• Perform 2’s complement over a number twice yields the original number

– Get 2’s complement by using instructions

MOV A, #6EH
CPL A ; 1’s
1’ complement
l t
INC A
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ARITHEMETIC: UNSIGNED NUMBER SUBTRACTION

• Multiple bytes subtraction (demo)

– Example: find 2762H – 1296H, store the lower byte in R7, higher byte in R6
CLR C
MOV A, #62H
SUBB A, #96H ; 62H-96H = CCH with CY = 1
; CY = 2 indicate there is a borrow
MOV R7, A
MOV A, #27H
SUBB A, #12H
MOV R6, A

– Note:
• In SUBB, the destination must be register A
 10

AIRTHEMETIC: UNSIGNED MULTIPLICATION AND DIVISION

• Multiplication
– MUL AB ; A * B, put the higher byte in B and lower byte in A
– Example
MOV A, #25H
MOV B, #65H
MUL AB ; 25H * 65H = E99
; B = 0EH, A = 99H
• Division
– DIV AB ; A/B, put quotient in A, and remainder in B
– Example
MOV A, #95
MOV B, #10
DIV AB ; A = 09, B = 05
– If the denominator (B) is 0, OV =1 to indicate there is an error.
 11

AIRTHEMETIC: UNSIGNED MULTIPLICATION AND DIVISION

• Example
– Converting a HEX number to decimal
• Review: HEX to decimal conversion: keep divide hex by 10 and keep the
remainder
i d

MOV A, #0FDH ; 253 decimal

MOV B, #10
DIV AB ; 253/10, (A) = 25, (B) = 3
MOV R7, B ; save lower digit
MOV B, #10
DIV AB ; 25/10, (A) = 2, (B) = 5
MOV R6, B ; save the next digit
; quotient (2) is less than 10
MOV R5, A ; save the last digit
 12

OUTLINE

• Arithmetic instructions

• Signed number operations

• Logic and compare instructions

• Rotate instruction and data serialization

• BCD, ASCII
 13

SIGNED NUMBER
• Signed 8-bit number
– MSB represent sign: ‘1’ negative, ‘0’ positive
– If positive, range is 0 to 127 (00000000 ~ 01111111)
– If negative,
negative use 2’s
2 s complement to find absolute value
• Example: a signed number is represented as 1111 1011, find its decimal value

– If a number is negative:
g it’s signed
g number representation
p = 2’s complement
p of its absolute
value
• Example: find the signed number representation of -1 and -128

– The range of 8-bit signed number is -128 – 127

• -128: 1000 0000
• -127: 1000 0001
• …
• -1: 1111 1111
• 0: 0000 0000
• 1: 0000 0001
• …
• 127: 0111 1111
 14

SIGNED NUMBER: OVERFLOW

• Overflow might happen during signed number operation
– Example
MOV A, #+96 ; 60H
MOV R1, #+70 ; 46H
ADD A, R1

– The result is larger than +127 Æ overflow

– The CPU will set OV = 1 to indicate overflow.
– CPU will set OV to 1 in the following conditions
• There is a carry from D6 to D7 but no carry out of D7 (CY = 0)
• There is a carry from D7 out but no carry from D6 to D7
– If there is carry from both D6 to D7 and D7 out
out, OV = 0
 15

SIGNED NUMBER: OVERFLOW

• Examples: find the OV flag in the following examples
– 1. MOV A, #-128
MOV R4, #-2
ADD A
A, R4

– 2.
2 MOV A
A, ##-2
2
MOV R1, #-5
ADD A, R1

– 3. MOV A, #+7
MOV R1,, #+18
ADD A, R1
 16

OUTLINE

• Arithmetic instructions

• Signed number operations

• Logic and compare instructions

• Rotate instruction and data serialization

• BCD, ASCII
 17

LOGIC INSTRUCTIONS
• ANL (and logic)
– ANL destination, source ; (dest) = (dest) AND (src)
– Bit by bit AND operation
• ORL (or logic)
– ORL destination, source ; (dest) = (dest) OR (src)
– Bit by bit OR operation
• XRL (xor logic)
– XRL destination, source ; (dest) = (dest) XOR (src)
– Bit by
y bit XOR operation
p
• Example
MOV A, #15H
MOV R0, #3CH
ANL A, R0
XOR A, R0
ORL A, R0
 18

COMPARE INSTRUCTIONS
• CJNE (compare and jump if not equal)
– CJNE destination, source, target
– If destination z source, jump to target
• If destination >= source, set CY =0
• If destination < source, set CY = 1
– Example: assume P1 is connected to a temperature sensor. Write a program to
continuously
ti l readd the
th temperature
t t andd test
t t it for
f the
th value
l off 75.
75
• If T = 75, then A = 75; if T < 75, then R1 = T; if T > 75, then R2 = T

– Self study: Example 6-27 (p.160)

 19

OUTLINE

• Arithmetic instructions

• Signed number operations

• Logic and compare instructions

• Rotate instruction and data serialization

• BCD, ASCII
 20

ROTATION
• RR (rotate the bits to the right)
– RR A ; can only be used with register A
– Cyclically rotate the bits of A to right
– Example
MOV A, #36H
RR A
RR A
• RL (rotate the bits to the left)
– RL A ; can only be used with register A
– Cyclically rotate the bits of A to left
– Example
MOV A, #2CH
RL A
RL A
 21

ROTATION
• RRC (rotate right through carry)
– RRC A ; can only be used with A
– Rotate right through carry
• RLC (rotate left through carry)
– RLC A ; can only be used with A
– Rotate left through carry

– Example
CLR C
MOV A, #26H
RRC A
SETB C
MOV A, #15H
RRL A
 22

ROTATION: SERIALIZING DATA

• Serializing data
– Transfer data one bit at a time.
– Example: write a program to transfer 41H serially via pin 2.1. Put two highs at
the
h start andd endd off the
h data.
d Send
S d the
h bbyte LSB fi
first.
 23

ROTATION: SWAP
• SWAP
– SWAP A ; can only be used with A
– Swap the lower nibble with the higher nibble

– Example
MOV A
A, #23H
SWAP A
 24

OUTLINE

• Arithmetic instructions

• Signed number operations

• Logic and compare instructions

• Rotate instruction and data serialization

• BCD, ASCII
 BCD AND ASCII
• Binary, BCD and ASCII
– Some devices use packed BCD to represent number
• E.g. timer uses packed BCD to keep track of time
– Some devices use binary number (hex) to represent number
• E.g. sensor represent temperature in binary format
– The display device usually accepts ASCII code
• E.g. In order to display the character in LCD, we need to send the ASCII
code to the display device
– Usually we need to perform conversion between BCD, Binary, and ASCII

Unpacked BCD Æ ASCII: add 30H to unpacked BCD

ASCII Æ unpacked BCD: Mask out the upper nibble of ASCII

BCD AND ASCII: BCD Î ASCII
• P k d BCD tto ASCII conversion
Packed i
– Packed BCD Æ unpacked BCD Æ ASCII
– From unpacked BCD to ASCII: add 30H to unpacked BCD
– E.g.
Eg

– E.g. Assume Reg. A has a packed BCD. Convert it to two ASCII codes and
place them in R2 and R6.
MOV A, #29H ; packed BCD
MOV R2, A ; keep a copy of BCD in R2
ANL A, #0FH ; low nibble Æ unpacked BCD
ADD A, #30H ; unpacked BCD Æ ASCII
MOV R6, A ; save the ASCII of low nibble to R6

MOV A, R2 ; get the original BCD

ANL A, #F0H ; get high nibble
SWAP A ; unpacked BCD
ADD A,
A #30H ; unpacked BCD Æ ASCII
MOV R2, A
BCD AND ASCII: ASCII Î BCD
• Convert ASCII to packed BCD

– ASCII Æ unpacked BCD: mask upper nibble with 0

– Unpacked BCD Æ packed BCD: combine two lower nibble to 1 byte
– Example:
p convert the ASCII code “47” to a ppacked BCD
MOV A, #’4’
ANL A, #0FH ; mask out upper nibble, unpacked BCD
SWAP A
MOV B, A ; store results in B

MOV A,, #’7’

ANL A, #0FH ; mask out upper nibble, unpacked BCD

ORL A,, B ; combine two nibbles into one byte

y
BCD AND ASCII: LOOK UP TABLE FOR ASCII
• Using look up table for ASCII
– Commonly used in interfacing with keypad and LCD
– Example: P0.0, P0.1, P0.2 are connected to 3 switches. Write a program to
send
d the
h ASCII code
d ‘0’
‘0’, ‘1’
‘1’, … ‘7’ to P2 bbased
d on the
h combination
bi i off theh 3
switches.
MOV DTPR, #MYDATA
MOV A,
A P1 ; read switches
ANL A, #07H ; mask all but lower 3 bits
MOVC A, @A+DPTR ; A is the index into LUT
MOV P2, A
SJMP $ ; stay
t here
h

ORG 400H
MYDATA: DB ‘0’, ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, ‘6’, ‘7’
BCD AND ASCII: BINARY Î ASCII
• Bi
Binary to
t ASCII conversion
i
– Many analog-to-digital converter provide output data in binary (hex) format
– To display the data, we need to convert it to ASCII
– 1 binary Æ unpacked BCD
Two steps: 1. BCD, 22. unpacked BCD Æ ASCII
– Example:
;----- main program------
ORG 0
ACALL BIN_2_DEC
ACLL DEC_2_ASCII

;-----BIN_2_DEC--------
BIN 2 DEC
BIN_2_DEC:
MOV A, #235 ; (A) = 0EBH
MOB B, #10
DIV AB ; (A) = 23, (B) = 5
MOV R0 R0, B ; (R0) = 5 = 05H
05H, unpacked BCD
MOV B, #10
DIV AB ; (A) = 2, (B) = 3
MOV R1, B ; (R1) = 3 = 03H, unpacked BCD
MOV R2, A ; (R2) = 2 = 02H, unpacked BCD
RET
BCD AND ASCII: BINARY Î ASCII
• Binary to ASCII conversion (Cont’d)
; ---------BCD 2 ASCII
DEC_2_ASCII:
MOV A,, R0 ; (A)
( ) = 05H
ORL A, #30H ; BCD Æ ASCII
MOV R0, A ; (R0) = ‘5’

MOV A
A, R1 ; (A) = 03H
ORL A, #30H ; BCD Æ ASCII
MOV R1, A ; (R1) = ‘3’

MOV A
A, R2 ; (A) = 02H
ORL A, #30H ; BCD Æ ASCII
MOV R2, A ; (R2) = ‘2’

• Self-study: checksum byte in ROM (p.170)