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Unit-3 Topics, , (According to BTEUP Syllabus, 2020), , • Arithmetic Operations, • Addition Subtraction Algorithm, • Multiplication Algorithm (Booth’s Algorithm), • Division Algorithm

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Division, Algorithm, Basic Terms, , 9÷2 =4 &1, Dividend, , Divisor, , Shift Left, 11000010, , 10000100, , Quotient, , Remainder

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Division Algorithm…(Continue), •, , Flow chart of division, Algorithm.(Restoring Algorithm), , Q= Dividend (in n bit), M= Divisor (in n+1 bits), A= Accumulator(in n+1 bits), Count = n (No .of bits in Dividend Q), If Q=12=1100 (represented in 4 bits ), M=3= 00011 (represented in 5 bits ), A= 00000(represented in 5 bits ), Count=4, Q3 Q 2 Q1, Q0, MSB, , Q=1010, , LSB, , 0, , MSB of A?, , 1, , Note: “A=A+M “also, called restoring of A

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Division Algorithm…(Continue), Example:, , 11 ÷ 3, , Here Dividend Q=11 or (1011)2, Divisor M= 3 or (00011)2, Count=4 and A=00000, 2’s Complement of M=(11101)2, Count, , A, , Q, , Action, , 4, , 00000, , 1011, , Initialization, , 00001, , 011_, , Shift AQ, , 00001+11101, =, , 011_, , A=A-M, , 0110, , MSB of A =1 so, set LSB of Q=0, and restore A, Count=Count-1, , 11110, 3, , 00001, , Q= Dividend (in n bit), M= Divisor (in n+1 bits), A= Accumulator(in n+1 bits), Count = n (No .of bits in Dividend Q), , 0, , MSB of A?, , 1

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Count, , A, , Q, , Action, , 00010, , 110_, , Shift left AQ, , 00010+11101, =, , 110_, , A=A-M, , 1100, , MSB of A =1 so set, LSB of Q=0 and, restore A, , Division Algorithm…(Continue), , 11111, , 2, , 00010, , Q= Dividend (in n bit), M= Divisor (in n+1 bits), A= Accumulator(in n+1 bits), Count = n (No .of bits in Dividend Q), , Count=count-1, , Discard, , Count, , A, , Q, , Action, , 00101, , 100_, , Shift left AQ, , 00101+11101, =, , 100_, , A=A-M, , 100010, 00010, , 1001, , MSB of A =0 so set, LSB of Q=1, Count=count-1, , Count, , A, , Q, , Action, , 00101, , 001_, , Shift left AQ, , 00101+11101, =, , 001_, , A=A-M, , 0011, , MSB of A =0 so set, LSB of Q=1 aand, Count=count-1, , Discard, , 1, , 100010, 0, , 00010, , 0, , MSB of A?, , 1

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Division Algorithm…(Continue), So the result is in A and Q where A holds remainder and Q holds, quotients., A=00010, and Q=0011, , 2, , 3, , 3) 11 ( 3, 9, 2

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Exercise, Try to do multiplication by your self…, 1) (12) ÷ (4), 2) (25) ÷ (4), Try to solve the question using algorithm.