cs281-hw1 - there is a repeated pattern point out what it...

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CS281 Introduction to Computer Architecture Homework 1 (20 points) Due date: Wednesday, September 3, 2008, 4:00pm. Note: Your homework must either be typed or clearly written. I will not grade the homework if it is unreadable. AIM : To understand positional number systems (e.g. Decimal number system, Binary number system, Hexadecimal number system, etc.); to understand conversion between decimal and other number systems, especially binary number system; to understand complement number system, and the way to get complement numbers… 1. Express the following decimal numbers as binary numbers. (3 points) (a) 123 (b) 600 (c) 341. Show your work. 2. Convert the following binary digits to hexadecimal notation. (2 points) (a) 100011101000 (b) 110100001 (c) 11111111 (d) 10011001101 3. Convert the following decimal numbers into radix-6 numbers. (4 points) (a) 138 (b) 207 (c) 1000 (d) 2050 4. Convert these two decimal numbers (with fraction) into binary numbers. (2 points) (a) 0.375 (b) 0.3 (If
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Unformatted text preview: there is a repeated pattern, point out what it is.) 5. Addition and subtraction. Suppose these are unsigned binary numbers. (1 points) (a) 111+1101 (b) 1000-11 6. Complement numbers. Suppose these are 4-bit 2’s complement numbers with four bits. Do the indicated operations. For subtraction, get the complement number of subtrahend first, then do addition. Tell if there is an overflow for each one. (3 points) (a) 1111+1110 (b) 0011 – 0010 (c) 1001 +1110 (d) 0100 + 0101 (e) 1111+0001 (f) 1111+1111 7. Complement numbers. (3 points) (a) What’s the range of the representable numbers in 2’s complement system if we use only 8 bits? (b) Do the following operations of 8-bit 2’s complement numbers and tell if there is an overflow. i) 00010010+11000100 ii) 10001000-01111111 8. Binary multiplication. Use the method (partial product + shifted multiplicand) we discussed in class. (2 points) 10101 x 11101...
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