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Unformatted text preview: LSU EE 27202 Homework 2 Solution Due: 28 September 2011 Solution updated :: 30 September 2011, 10:45:27 CDT (Solutions to 4b and 4c were swapped.) Problem 1: Perform the multiplications indicated below. Multiply the following two 8bit unsigned binary integers into a 16bit product: 01110010 + 10010011 . Solution: 01110010 = 0x72 = 114 10010011 = 0x93 = 147 01110010 < Pad with 0 zeros. 011100100 < Pad with 1 zero. 011100100000 < Pad with 4 zeros. 011100100000000 < Pad with 7 zeros. 0100000101110110 < Binary to the right, below show in hex and decimal. 0100 0001 0111 0110 = 0x4176 = 16758 Multiply the following two 8bit signed 2s complement integers into a 16bit product: 01110010 + 10010011 . Solution: Binary numbers broken into groups of 4 digits for readability. 0111 0010 = 0x72 = 114 Multiplicand 1001 0011 = 01101100 + 1 = 01101101 => 109 0111 0010 < Pad with 0 zeros. 0 1110 0100 < Pad with 1 zero. 0111 0010 0000 < Pad with 4 zeros. 1100 0111 0000 0000 < Pad with 7 zeros. Used negated and sign ext mcand 1100 1111 0111 0110 < Product 11 0000 1000 1010 < Twos comp of product: 0x308a = 12426, so prod is 12426 How last partial product obtained: 0111 0010 < Multiplicand 1000 1110 < Negated Multiplicand (2s complement) 100 0111 0000 0000 < Pad on left with 7 zeros. 1100 0111 0000 0000 < Make 16bit by sign extension (repeating sign bit). The theorem numbers in the problems below are from Dr. Skavantos Handout 5, available via http://www.ece.lsu.edu/alex/EE2720/EE2720_HO5.pdf . Problem 2: Prove the following ( a ) Prove theorem T5 (called complement in the notes, but a better name is the damnedifyou do,damnedifyoudont theorem) by perfect (finite) induction....
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