HW1_Soltn - +01111001 11110010 OVERFLOW (sum of two...

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9/09/09 SOLUTION ECSE-2610 COCO: HW # 1 9/9/09 ECSE-2610 Computer Components and Operations Homework # 1 Due Wednesday, September 9, 2009 in studio Individual activities. Show your calculations. 1. (3 points) Give the sign-magnitude binary form of: (a) +12 10 (8 bits) = 0000 1100 (b) -12 10 (8 bits) = 1000 1100 (c) -121 10 (8 bits) = 1111 1001 2. (3 points) Convert to two’s-complement binary form: (a) +12 10 (8 bits) = 0000 1100 (b) -12 10 (8 bits) = 1111 0100 (c) -121 10 (8 bits) = 1000 0111 3. (4 points) Convert the following decimal numbers to binary form with 4 bits before and 4 bits after the binary point: (a) 2.75 = 0010.1100 (b) 13.375 = 1101.0110( 4. (6 points) Binary addition and subtraction in 8-bit sign-magnitude form Check for overflow. (a) 00110110 +00101001 01001111 (b) 00110110 -00101001 00001101 (C) 00101001 -00110110 10001101 (d) 01111001 +11111001 00000000 (or 10000000) (e) 01111001
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Unformatted text preview: +01111001 11110010 OVERFLOW (sum of two positive integers > 111 1111) (f) 11111001 +11111001 11110010 OVERFLOW (sum of two negative integers < 1 111 1111) 9/09/09 SOLUTION ECSE-2610 COCO: HW # 1 9/9/09 5. (4 points) Perform the following additions of 2s complement numbers, showing all the carries. Verify the addition by converting to decimal. (a) 0011 1110 + 0011 0111 0111 0101 = 62+55 = 117 (b) 1100 0011 + 0110 0101 0010 1000 = -61 + 101 = 40 6. (5 points) (a) What is the largest 12-bit sign-magnitude number? 0111 1111 1111 = 2047 (b) What is the smallest (i.e., negative) 12-bit sign-magnitude number? 1111 1111 1111= -2047 (c) What is the largest 12-bit 2s complement number? 0111 1111 1111 = 2047 (d) What is the smallest 12-bit 2s complement number? 1000 0000 0000 0000 = -2048 (e) How many different values can be represented with 10 bits? 1024...
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This note was uploaded on 03/03/2010 for the course ECSE 2610 taught by Professor Ji during the Spring '08 term at Rensselaer Polytechnic Institute.

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HW1_Soltn - +01111001 11110010 OVERFLOW (sum of two...

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