TUTORIAL -1 COMPUTER ORGANISATION TIT-402

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1 TUTORIAL -1 COMPUTER ORGANISATION TIT-402 Q1.(43) 10 = (? ) 2 s (GATE 2000) a) b) c) d) Q2.The 2 s complement representation of (-539) 10 in hexadecimal is (GATE 2001) a)abe B)DBC c)de5 d) 9E7 Q3. The decimal value 0.25 (GATE 2002) (a) is equivalent to the binary value 0.1 (b) is equivalent to the binary value 0.01 (c) is equivalent to the binary value (d) cannot be represented precisely in binary Q4. The 2 s complement representation of the decimal value 15 is (GATE 2002) (a) 1111 (b) (c) (d) Q5. In 2 s complement addition, overflow (GATE 2002) (a) is flagged whenever there is carry from sign bit addition (b) cannot occur when a positive value is added to a negative value (c) is flagged when the carries from sign bit and previous bit match (d) None of the above Q6. Assuming all numbers are in 2 s complement representation, which of the following numbers is divisible by ? (A) (B) (C) (D) Q7. Find the following differences using twos complement arithmetic: a b c

2 d Q8. Is the following a valid alternative definition of overflow in twos complement arithmetic? If the exclusive-or of the carry bits into and out of the leftmost column is 1, then there is an overflow condition. Otherwise, there is not. Q9. Represent the following twos complement values in decimal: ; Q10. Represent the following decimal numbers in both binary sign/magnitude and twos complement using 16 bits 1) ) -14 Q11.the unsigned ( ) 2 =(? ) 10 a)63 b)91 c) 92 d)13 Q12.Which has the largest value? A)(110) 10 b) ( ) 2 c)(1111) 2 d)(9a) 16 e) (222) 8 Q13.What is the weight of digit 3 in base 7 number 12345? a)3 b)5 c)7 d)14 e)49 Q14.if (321) 4 =(57) 10 What is the decimal equivalent of ( ) 4 a)57 x 10 5 b) 57 x 10 4 c) 57 x 4 5 d) 57 x 4 10 Q15. The unsigned binary number (110001) 2 is equal to (? ) 8 a)49 b)61 c)31 d)15 e)none of the above Q16.In 6 bit 1 s complement binary no system,what is the decimal value represented by (010100) 1s a)-11 b)43 c)-43 d)20 e)-20 Q17.In 6 bit 2 s complement binary no system,what is the decimal value represented by (100100) 2s a)-4 b)36 c)-36 d)-27 e)-28 Q18.For 2 s complement binary number,the range of values for 5 bit numbers is a)0 to 31 b) -8 to +7 c)-8 to -8 d) -15 to -15 e) -16 to +15 Q19.For 4 bit 2s complement scheme,what is the result of this (1011) 2s + (1001) 2s

3 a.0100 b c d.1001 e.overflow Q20. (1217) 8 is equivalent to (GATE 2009) (A) (1217) 16 (B) (028F)16 (C) (2297)10 (D) (0B17)16 Q21. If 73 x (in base x number system)=54 y, (in base y number system),then possible values of x and y are a)8,16 b)10,12 c) 9,13 d)8,11 (GATE 2004) Q22.Let A= and B= be two 8 bit 2 s complement no s.their product in 2 s complement is a) b) c) d) (GATE 2004) Q23.The hexadecimal representation of (657) 8 is (GATE 2005) a)1af b) D78 c)d71 d)32f Q24. how many kilobytes are accessible with a 23-bit address space? A)2^23 KB B)2^23 Kb C)2^13 KB D)2^13Kb Q25. Represent each of the following using the 8-bit two's-complement integer representation. a. 10 (10) b. 60 (10) c. 104 (10) Q26. For the following, assume a six-bit two's-complement representation of integers. a. What numeric value does represent? b. What numeric value does represent? c. What bit pattern is used to represent 12 (10)? Q27. a. What is the smallest (most negative) number you can represent in seven bits using signmagnitude representation? Give both the bit pattern of the number and its base-10 translation. b. Answer the same question for a seven-bit two's-complement representation.

4 Q28. What would be the bias value for a. A base-2 exponent in a 6-bit field? b. A base-8 exponent in a 7-bit field? Q29. It is said that a 32-bit format can represent a maximum of different numbers. How many different numbers can be represented in the IEEE 32-bit format? Explain. Q30.Express the following numbers in IEEE 32-bit floating-point format: a)-5 b) -6 c) -1.5 d) 384 e) 1/16 f)-1/32 G)1.0 H)-1.0 I) (438F0000) 16 Q31. The following numbers use the IEEE 32-bit floating-point format.what is the equivalent decimal value? a b c Q32. Express the following numbers in IBM s 32-bit floating-point format, which uses a 7-bit exponent with an implied base of 16 and an exponent bias of 64 (40 hexadecimal).a normalized floating-point number requires that the leftmost hexadecimal digit be nonzero; the implied radix point is to the left of that digit. Q33.A hypothetical computer stores floationg point numbers in 7 bits.th e first bit is used for sign of number,the next three for the biased exponent and the next three for the magnitude of the mantissa.the number ( ) 2 represented in base 10 is a)0.375 b)0.875 c) 1.5 d) 3.5 Q34. A hypothetical computer stores floationg point numbers in 7 bits.th e first bit is used for sign of number,the next three for the biased exponent and the next three for the magnitude of the mantissa.you are asked to represent in the above word.the error in this case would be a)underflow b)overflow c)nan d) No error Q35. Consider the following 32-bit floating-point representation scheme as shown in the formal below. A value is specified by 3 fields, a one bit sign field (with 0 for positive and 1 for negative values), a 24 bit fraction field (with the binary point being at the left end of the fraction bits), and a 7 bit exponent field (in excess-64 signed integer representation, with 16 being the base of exponentiation). The sign bit is the most significant bit.

5 (a) It is required to represent the decimal value 7.5 as a normalized floating point number in the given format. Derive the values of the various fields. Express your final answer in the hexadecimal. (b) What is the largest values that can be represented using this format? Express your answer as the nearest power of 10. (GATE 2002) Q36. The following is a scheme for floating point number representation using 16 bits (GATE 2003) Let s, e, and m be the numbers represented in binary in the sign, exponent, and mantissa fields respectively. Then the floating point number represented is: _ What is the maximum difference between two successive real numbers representable in this system? Q37.Explain why, in a computer, floating point mathematics may not be associative or distributive, i.e. (A+B)+C may not equal A+(B+C). Q38.We use negative numbers,positive numbers in computer,then it seems that unsigned numbers are of no use in computer So What is the application of unsigned numbers? General Questions

6 Q39. If a CPU has a clock frequency of 3.2 GHz, how long (in ns) does one access cycle take? Q40.Are hardware and software equivalent? Can you really do anything in hardware that you can do in software, and vice-versa? Examples? Q41.What are the three basic-level pieces of a digital computer? Q42.Give two reasons why you can't store 12GB of system memory on a hard drive with an advertised capacity of 12GB.

CS 265. Computer Architecture. Wei Lu, Ph.D., P.Eng.

CS 265. Computer Architecture. Wei Lu, Ph.D., P.Eng. CS 265 Computer Architecture Wei Lu, Ph.D., P.Eng. 1 Part 1: Data Representation Our goal: revisit and re-establish fundamental of mathematics for the computer architecture course Overview: what are bits