hw2 - Department of Systems Engineering and Engineering...

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Unformatted text preview: Department of Systems Engineering and Engineering Management ERG 2020 C/D Digital Logic and Systems Instruction: Question 1. THE CHINESE UNIVERSITY OF HONG KONG Show your work clearly. Assignment 2 Perform the following 8-bit signed binary number arithmetic and identify over ow, if any. (a) 0100 1110 + 1101 0011 (ones'-complement representations) (b) 0100 1110 1101 0011 (ones'-complement representations) (c) 0100 1110 + 1101 0011 (excess-127 representations) (d) 0100 1110 1101 0011 (excess-127 representations) Perform the following unsigned binary-coded decimal number arithmetic. (a) 0101 1001 0001 + 0011 0111 0110 (b) 0101 1001 0001 0011 0111 0110 Question 3. Question 2. (a) Convert the decimal number 1 261 101 to binary oating-point number with 8 binary places in normalized scienti c notation (use rounding if necessary). (b) Convert the binary number 1 01101001 22 to decimal oating-point number with 4 decimal places in normalized scienti c notation (use rounding if necessary). : : Suppose that a particular machine uses 8 bits to represent a binary oating-point number in scienti c notation with the following convention: bit 7 (1 bit) represents the sign ; bits 6{4 (3 bits) represent the exponent in excess-3 representation; bits 3{0 (4 bits) represent the mantissa (with rounding). Find the representations of the following decimal numbers in that machine (use rounding if necessary). (a) 0 34 (b) 12 61 (You may use the result in Question 3(a).) S E F : : Question 4. Perform the following arithmetic and give the answers in binary oating-point numbers with 8 binary places in scienti c notation (use rounding if necessary). (a) 1 11011101 24 + 1 10011011 22 (b) 1 00000101 23 1 11101001 2 1 : : : : Question 5. ...
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This note was uploaded on 11/13/2010 for the course SEEM SEEM2018 taught by Professor Chan during the Spring '10 term at CUHK.

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