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EECC201 Freshman Seminar Intro to Micro controller Dr. Ken Hsu WEEK 7 ADDITION, SUBTRACTION AND COMPARE OF BINARY NUMBERS Important: Irritant sounds may be heard during browsing. Better turn the volume off.

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Binary numbersUnsigned decimalSigned DecimalHexadecimal 0000000 0001111 0010222 0011333 0100444 0101555 0110666 0111777 10008-88 10019-79 101010-6A 101111-5B 110012-4C 110113-3D 111014-2E 111115-1F

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2’S COMPLEMENT 0100 Take 1’s complement 1011Add 1 to result 1 + 1100Get 2’s complement

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To distinguish between two numbers with the same sign and two numbers with different signs in assembly language programming ANDNum1,#80H ANDNum2,#80H XORNum1,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.

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ADDITION Unsigned number addition (1)Numbers with same sign (a)Positive c 1111 111115 101111 1101026 CY flag set to 1 This means that more than 4 bit is needed to represent sum. Carry 1 bit + 1 XOR 1 = No overflow

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ADDITION Signed number addition (1)Numbers with same sign (a)Negative 1111 1111-1 1011-5 11010-6 + 1 XOR 1 = No overflow CY flag set to 1 Ignore carry since there is no overflow

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ADDITION Signed number addition (1)Numbers with different sign 1000-8 0111+7 01111-1 + CY flag set to 0

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SUBTRACTION (COMPARE CMP) Unsigned number subtraction (1)Numbers with different sign 0011+3 1011-5 - Do 2’s Complement with second number and add with first number 01 0011 0101 010008 + Carry is 0. Make sign bit positive and thus equal to 8 and not -8. 0 XOR 1 = overflow

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SUBTRACTION (COMPARE CMP) Unsigned number subtraction (1)Numbers with same sign (a)Positive 111115 101111 - Do 2’s Complement with second number and add with first number 1111 0101 101004 + Ignore carry since there is no overflow 1 XOR 1 = No overflow

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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 1111 0101 101004 + Ignore CY since there is no overflow 1 XOR 1 = No overflow

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SUBTRACTION (COMPARE CMP) Unsigned number subtraction (1)Numbers with different sign 1000-8 0111+7 - Do 2’s Complement with second number and add with first number 10 1000 1001 10001-15 + Overflow. This means that more than 4 bit is needed to represent number. 1 XOR 0 = overflow

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AVERAGE OF 2 NUMBERS NOTE: If the average of a positive number gives a fraction, round fraction down. 111115 101111 1111 11010 + 26Rotate right with carry by 1 bit. RORC 0110113 (1) Average of a positive number with a whole result

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10008 01117 01111 + 15Rotate right with carry by 1 bit. RORC 01117.5 (1) Average of a positive number with a fractional result. AVERAGE OF 2 NUMBERS NOTE: If the average of a positive number gives a fraction, round fraction down. 7

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1111-1 1011-5 11010 + -6Rotate right with carry by 1 bit. RORC 01101-3 (1) Average of a negative number with a whole result. AVERAGE OF 2 NUMBERS NOTE: If the average of a negative number gives a fraction, round fraction down. 1111

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1000-8 0111+7 01111 + Rotate Right with carry by 1 bit. RORC 11111 -0.5 (1) Average of a negative number with a fractional result. AVERAGE OF 2 NUMBERS NOTE: If the average of a negative number gives a fraction, round fraction down. 11111 NOT1 CY

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