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HCS12 Arithmetic Lecture 3.3

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68HC12 Arithmetic Addition and Subtraction Shift and Rotate Instructions Multiplication Division

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Addition and Subtraction

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HCS12 code for 1+, 2+ ;1+ ( n -- n+1 ) ONEP LDD0,X ADDD#1 STD0,X RTS ;2+ ( n -- n+2 ) TWOP LDD0,X ADDD#2 STD0,X RTS

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HCS12 code for 1-, 2- ;1- ( n -- n-1 ) ONEP LDD0,X SUBD#1 STD0,X RTS ;2- ( n -- n-2 ) TWOP LDD0,X SUBD#2 STD0,X RTS

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Double Numbers

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Adding Double Numbers

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Subtracting Double Numbers

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68HC12 Arithmetic Addition and Subtraction Shift and Rotate Instructions Multiplication Division

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Logic Shift Left LSL, LSLA, LSLB 0 1 0 1 0 0 1 0 1 1 C 76543210Bit 1 0 1 0 0 1 0 1 10 C 76543210Bit 1 0 1 0 0 1 0 1 76543210 AB LSLD

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Logic Shift Right LSR, LSRA, LSRB 1 0 1 0 0 1 0 1 10 C 76543210Bit 1 0 1 0 0 1 0 1 10 C 76543210Bit 1 0 1 0 0 1 0 1 76543210 AB LSRD

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Arithmetic Shift Right ASR, ASRA, ASRB 1 0 1 0 0 1 0 1 1 C

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Rotate Left ROL, ROLA, ROLB 1 0 1 0 0 1 0 1 1 C 76543210Bit

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Rotate Right ROR, RORA, RORB 1 0 1 0 0 1 0 11 C 76543210Bit

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2*, 2/, and U2/

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68HC12 Arithmetic Addition and Subtraction Shift and Rotate Instructions Multiplication Division

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Binary Multiplication

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13 x 12 26 13 156 1101 1100 0000 1101 10011100 9 C = 156

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Hex Multiplication

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61 x 90 5490 3D x 5A 262 A x D = 82, A x 3 = 1E + 8 = 26 131 5 x D = 41, 5 x 3 = F + 4 = 13 1572 16 = 5490 10 Dec Hex

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Hex Multiplication product = $1572 is in D = A:B ; multiply 8 x 8 = 16 =00004000 ORG $4000 4000 86 3D LDAA #$3D 4002 C6 5A LDAB #$5A 4004 12 MUL

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product = $1572 is in D = A:B

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Multiplication

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16-Bit Hex Multiplication 31A4 x1B2C 253B0 4 x C = 30 A x C = 78 + 3 = 7B 1 x C = C + 7 = 13 3 x C = 24 + 1 = 25

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16-Bit Hex Multiplication 31A4 x1B2C 253B0 6348 2 x 4 = 8 2 x A = 14 1 x 2 = 2 + 1 = 3 2 x 3 = 6

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16-Bit Hex Multiplication 31A4 x1B2C 253B0 6348 2220C 4 x B = 2C A x B = 6E + 2 = 70 1 x B = B + 7 = 12 3 x B = 21 + 1 = 22

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16-Bit Hex Multiplication 31A4 x1B2C 253B0 6348 2220C 31A4 0544D430 ORG $4000 4000 CC 31A4 LDD #$31A4 ;D = $31A4 4003 CD 1B2C LDY #$1B2C ;Y = $1B2C 4006 13 EMUL ;Y:D = D x Y

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Y:D = 0544D430

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Multiply Instructions Note that EMUL and MUL are unsigned multiplies EMULS is used to multiply signed numbers

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Unsigned Multiplication Dec Hex 65528 x 8 524224 FFF8 x 0008 7FFC0 524224 10 = 7FFC0 16

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FFF8 x 0008 7FFC0

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Unsigned Multiplication Dec Hex 65528 x 8 524224 FFF8 x 0008 7FFC0 524224 10 = 7FFC0 16 But FFF8 = 1111111111111000 can be a signed number 2’s comp = 0000000000001000 = $0008 = 8 10 Therefore, FFF8 can represent -8

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Signed Multiplication Dec -8 x 8 -64 64 10 = 00000040 16 = 0000 0000 0000 0000 0000 0000 0100 0000 2’s comp = 1111 1111 1111 1111 1111 1111 0100 0000 = $FFFFFF40 Therefore, for signed multiplication $FFF8 x $0008 = $FFFFFF40 and not $7FFC0 The EMULS instruction performs SIGNED multiplication

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Signed Multiplication product = $FFFFFFC0 is in Y:D ; EMULS signed 16 x 16 = 32 =00004000 ORG $4000 4000 CC FFF8 LDD #$FFF8 ;D = $FFF8 4003 CD 0008 LDY #$0008 ;Y = $0008 4006 1813 EMULS ;Y:D = D x Y

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product = $FFFFFFC0 is in Y:D

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Multiplication Note that EMUL is a 16 x 16 multiply that produces a 32-bit unsigned product. If the product fits into 16-bits, then it produces the correct SIGNED product.

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FFF8 x 0008 7FFC0 -8 x 8 -64 = $FFC0 Correct 16-bit SIGNED result

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Multiplication Even MUL can be used for an 8 x 8 = 8 SIGNED multiply

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Note: A x B = A:B B contains the correct 8-bit SIGNED value

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68HC12 Arithmetic Addition and Subtraction Shift and Rotate Instructions Multiplication Division

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Binary Division 100111001100 1 0111 1 1 1100 0011 0 0 0000 01100 1 1100 0000 D C 9C

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Hex Division EE BC2F C C x E = A8 C x E = A8 + A = B2 B28 9AF A

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Hex Division EE BC2F C A x E = 8C A x E = 8C + 8 = 94 B28 9AF A 94C 63 Dividend = BC2F Divisor = EE Quotient = CA Remainder = 63

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Hex Division EE BC2F C B28 9AF A 94C 63 =00004000 ORG $4000 4000 CD 0000 LDY #$0000 4003 CC BC2F LDD #$BC2F 4006 CE 00EE LDX #$00EE 4009 11 EDIV ;BC2F/EE = CA rem 63

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Division

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Y:D/X => Y Remainder in D

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Divisor may be too small EE FFBC2F 11313 rem 85 Quotient does not fit in Y Overflow bit, V, will be set S X H I N Z V C Condition code register

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S X H I N Z V C Condition code register Note overflow bit, V, set N and Z are undefined Y and D unchanged

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S X H I N Z V C Condition code register Note divide by zero sets carry bit, C N, Z, and V are undefined Y and D unchanged

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Division

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Y:D/X => Y Remainder in D Note symmetric division Truncation toward zero Sign of remainder = sign of dividend

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Y:D/X => Y Remainder in D Note symmetric division Truncation toward zero Sign of remainder = sign of dividend

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Symetric Division (truncation toward zero) DividendDivisorQuotientRemainder 26 7 3 5 -26 7 -3 -5 26 -7 -3 5 -26 -7 3 -5 Floored Division (truncation toward minus infinity) DividendDivisorQuotientRemainder 26 7 3 5 -26 7 -4 2 26 -7 -4 -2 -26 -7 3 -5

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D = $0001 X = $0002 FDIV => X = $8000 D = $0000 1212 = 0.5 = 0.1000000000000000 2 = 0.8000 16

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D = $1234 X = $0010 IDIV => X = $0123 D = $0004

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D = $FFE6 X = $0007 IDIVS => X = $FFFD D = $FFFB -26 7 = -3 remainder = -5

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