# Tutorial 1 - (a 8-bit signed 2's complement representation...

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EE 2000 Logic Circuit Design, Semester A, 2007/08 Tutorial 1 The questions are divided into two levels. Level 1 is the basic level question. You should be able to answer them after completing the lecture. Level 2 is the advanced level question. You may have to take a research before answering them. Please be prepared before the tutorial. Level 1 Question 1: Complete the following table by converting the below numbers to decimal, binary, octal and hexadecimal number systems. Decimal Binary Octal Hexadecimal 33 11101101.01 250.8 Question 2: (a) What is the largest binary number that can be obtained with 16 bits? (b) What is its decimal equivalent? Question 3: Find the 1's and 2's complements of the following 8-digit binary numbers: (a) 0010 1010 (b) 1111 1111 Question 4: Perform the arithmetic operations (-128) + (-1) in binary using

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Unformatted text preview: (a) 8-bit signed 2's complement representation for negative numbers (b) 9-bit signed 2’s complement representation for negative numbers Does overflow happen? Why? Level 2 Question 5: Please calculate a + b , a- b , a · b , and a / b for the pair of binary numbers a = 10101 and b = 1011 without converting to decimal (Show your work and the carries) Question 6: Determine the value of x if (211) x = (152) 8 . Question 7: Formulate a simple procedure for converting base-4 numbers directly to hexadecimal number. Use the procedure to convert (12321) 4 to base 16. (Hints: 4 2 = 16) Question 8: In the lecture, we only discuss the r ’s-complement and ( r-1)’s-complement of an integer number. Find the 1’s complement and 2’s complement of the following fractional binary numbers. (a) 010.11 (b) 11011.100...
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Tutorial 1 - (a 8-bit signed 2's complement representation...

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