sam1 - numbers Given an n-digit system with base 8 deFne...

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CSE20 Exercise 1, January 26, 2010, Name 1. Convert 234 16 to binary. 2. Convert a binary number (110101) to a decimal number. 3. A hybrid system has 5 digits of radix 3 and 4 digits of radix 4. Describe the range of the system. 4. Write the truth table of a full subtracter with three binary inputs x, y, b in and two binary outputs b out , d . 5. Write the sequence of a 3-bit Gray code. 6. Describe the ranges of the signed magnitude representation, one’s complement representation, and two’s complement representation for 8-bit system. 7. Convert 66 10 to the 8-bit two’s complement representation. 8. Given x = 12 10 and y = 14 10 , show the operation of x - y with 6-bit one’s complement. 9. We have deFned and learned the idea of two’s complement for n-bit binary
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Unformatted text preview: numbers. Given an n-digit system with base 8, deFne the eight’s complement representation. Show the arithmetic of x-y where x = 11 8 and y = 15 8 with a 5-digit system in eigth’s complement representation. 10. Prove that 1 1 × 3 + 1 3 × 5 + ... + 1 (2 n-1)(2 n +1) = n 2 n +1 11. Given three integers x, y, d, prove that ( x + y )% d = ( x % d + y % d )% d , where % is a modulus operation. 12. Given three integers x, y, d, prove that ( x-y )% d = ( x % d-y % d )% d , where % is a modulus operation. 13. Given three integers x, y, d, prove that ( x % d × y % d )% d = ( x × y )% d , where % is a modulus operation. 1...
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This note was uploaded on 06/12/2011 for the course CS 1 taught by Professor Staff during the Fall '08 term at Cornell.

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