Birkbeck (University of London) Department of Computer Science and Information Systems. Introduction to Computer Systems (BUCI008H4)

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1 Birkbeck (University of London) Department of Computer Science and Information Systems Introduction to Computer Systems (BUCI008H4) CREDIT VALUE: none Spring 2017 Mock Examination SUMMARY ANSWERS Date: Tuesday 14th March 2017 Duration: NAME: There are seven questions in this paper. Answer all seven questions. Each question carries 10 marks in total. Calculators and other electronic devices are not permitted. The examination is closed book. No supplementary material is provided. This paper is not prior disclosed. BUCI008H4 Page 1 of 6 c Birkbeck College 2016

2 1. Show your working in all parts of this question. (a) Add the binary numbers and Answer: Two marks. One mark for the correct answer without any working. Subtract the binary number 1011 from the binary number Answer: Two marks. One mark for the correct answer without any working. Multiply 2 10, i.e. two to the power ten, and 2 13, i.e. two to the power thirteen. An answer in the form of a power of two is required. Answer: Two marks. One mark for the correct answer without any working such as 23 = (d) Convert the binary number to the corresponding decimal number. Answer: 22. Two marks. One mark for the correct answer without any working. (e) Convert the hexadecimal numbers A and B to the corresponding decimal numbers, add the decimal numbers and convert the result to hexadecimal form. Answer: A is decimal 10 and B is decimal 11. Add to obtain decimal 21, which is hexadecimal 15. Two marks 2. Show your working in all parts of this question. (a) Write out the table for the three bit excess notation for integers. Show clearly the integers which can be represented using the three bit excess notation. Answer: 4 marks. 1/2 mark for each correct entry in the following table Obtain the four bit two s complement representations for the integers -1 and 2. Obtain from these two s complement representations the two s complement representation for the integer 1. Note that -1+2 is equal to 1. Answer: 1111 and On adding these bit strings as if they are binary numbers the bit string is obtained. The rightmost 4 bits of are the two s complement representation for 1. 4 marks. One mark for each correct two s complement representation of -1, 2 and 1. One mark for a correct addition. Find two integers m, n with corresponding three bit excess representations s, t, such that i) m + n has a three bit excess representation u; and ii) u is not equal to the BUCI008H4 Page 2 of 6 c Birkbeck College 2016

3 rightmost three bits of the bit string obtained by adding s and t as if they were binary numbers. Answer: Two marks for any correct answer, e.g. m = 0, n = (a) State the name of one binary Boolean operation. Explain the meaning of the word binary in this context. Answer: Two marks for naming any binary Boolean operation such as AND, OR, Exclusive OR, etc. A truth table is not required. Two marks for stating that the term binary indicates that the Boolean operation acts on pairs of values. Four marks in total. Write out the truth table for the Boolean operation A == B. If A and B have the same value, then A == B is true (1 or T is also accepted), otherwise A == B is false (0 or F is also accepted). Answer: One mark for each correct row, making four marks in total. A B A == B Describe one way in which Boolean operations are used in programming languages. Answer: Boolean operations are used to make decisions about the flow of control in a program. Two marks. Two marks if the answer consists of a reasonable example. Relational operators such as < are not counted as Boolean operators. 4. The Brookshear floating point representation for a binary fraction x consists of eight bits, labeled s, e 1, e 2, e 3, m 1, m 2, m 3, m 4 from left to right. If x is zero, then all eight bits are zero. If x is strictly negative, then the sign bit s is 1. If x is strictly positive, then the bit s is zero. Next, suppose x is not zero. To obtain the remaining seven bits, x is written in the form ±2 r 0.t where r is an integer and t is a bit string such that the leftmost bit of t is 1. The bits e 1, e 2, e 3 together comprise the three bit excess notation for r and the bits m 1, m 2, m 3, m 4 of the mantissa are the leftmost four bits of t. (a) Obtain the Brookshear floating point representation for the decimal fraction 1/16. In your answer show the value of r and the value of the bit string 0.t. (8 marks) Answer: (four marks), r = 3 (two marks) and 0.t = (two marks), making eight marks in total. BUCI008H4 Page 3 of 6 c Birkbeck College 2016

4 Suppose that the Brookshear floating point representation for a non-zero number x is given. Explain how it is possible to obtain quickly the Brookshear floating point representation for the number 2x, under the assumption that the representation of 2x exists. Answer: Increase the exponent by 1. Two marks. One mark for an example without any statement of the general method. 5. The table included below in this question describes instructions of length 16 bits, made by concatenating an op-code and an operand. The first four bits record the op-code. The remaining 12 bits record the operand. Four bits are required to specify a register R and eight bits are required to specify a memory location XY. Each register holds eight bits and each memory location holds eight bits. Each 16 bit instruction is coded by four hexadecimal digits. For example, the four hexadecimal digits 37A9 specify an instruction with op-code 3, in which the 7 refers to register 7 and A9 refers to the memory cell A9. The registers are numbered in hexadecimal from 0 to F. All memory addresses in this question are given in hexadecimal notation. Op code Operand Description 1 RXY Load register R with the bit pattern in memory cell XY. 2 RXY Load register R with the bit pattern XY. 3 RXY Store the bit pattern in register R at memory cell XY. 4 0RS Move the bit pattern in register R to register S. 5 RST Add (two s complement) the bit patterns in registers R and S. Put the result in register T. 6 RST Add (floating point) the bit patterns in registers R and S. Put the result in register T. 7 RST Or the bit patterns in registers S and T. Put the result in register R. 8 RST And the bit patterns in registers S and T. Put the result in register R. 9 RST Exclusive Or the bit patterns in registers S and T. Put the result in register R. A R0X Rotate the bit pattern in register R one bit to the right X times. B RXY Jump to the instruction in memory cell XY if the bit pattern in register R is equal to the bit pattern in register 0. C 000 Halt. BUCI008H4 Page 4 of 6 c Birkbeck College 2016

5 (a) Describe the result of the instruction 9312 when register 1 contains A6 (in binary ) and register 2 contains F F (in binary ). Register 3 contains the bit string Four marks. Two marks for stating that the result appears in register 3 and two marks for the correct bit string. One mark if it is stated that the bits in register 1 are flipped without any further answer. Write a program in machine code to i) read the contents of the memory cell with the hexadecimal address 91 into register 1; then ii) flip the bits of the bit string in register 1 and put the resulting bit string in register 3; and finally iii) copy the bit string in register 3 to the memory cell with address 91. The bits in a bit string are flipped by converting 0 to 1 and 1 to 0. For example, if the bit string is , then flipping the bits yields the bit string (6 marks) Answer: FF Six marks. Any reasonable answer accepted, including 1191, 9312, 3391 in which it is assumed that register 2 already contains FF. Two marks deducted for each mistake. 6. (a) Give a definition of the term algorithm. Give a definition of the term variable, as this term might be used when describing an algorithm. Answer: An algorithm is an ordered sequence of unambiguous executable steps that defines a terminating process. Two marks. Two marks for any reasonable variation in this wording. For example, an algorithm is a finite sequence of executable instructions. A variable is a named memory location or a variable is a quantity that has a name and a value. Either answer is accepted. Two marks. State one advantage in using a high level programming language to implement algorithms. Answer: An algorithm can be programmed using fewer instructions than would be required in a machine code version of the same algorithm. Two marks. Any reasonable answer accepted. Consider the following statement. To convert degrees centigrade into degrees Fahrenheit, multiply by 9/5 and add 32. This statement is to be the basis for an algorithm. Identify the input and the output of the algorithm. Suggest two variables that might be used in an implementation of this algorithm. Answer: The input is a number of degrees centigrade. The output is the corresponding number of degrees Fahrenheit. The two variables could be the number c of degrees centigrade and the number f of degrees Fahrenheit. Four marks. One mark for each item. BUCI008H4 Page 5 of 6 c Birkbeck College 2016

6 7. Recall that an array is a block of values of the same type, for example, A = ( 1 2 ) The indexing of the rows and columns of an array starts in each case from 0 and the index for the rows is given first. For example, A[0, 1] has the value 2. (a) Describe one way in which the array A might be stored in a computer memory. Use a diagram to show clearly where the different values in A are placed. You may assume that each entry of A is stored in a single memory cell. Answer: row major order is assumed in this answer but other arrangements, e.g. column major order, are accepted. The rows of A are placed in memory side by side. Four marks. Full marks given for a diagram If the memory cell for the value 1 is x then what is the memory cell for the value 9? Answer: x + 4. Two marks Let x be the memory cell in which A[0, 0] is stored. Show how the location of the memory cell holding A[i, j] can be calculated using the values of x, i and j. Answer: x + 3i + j. Four marks. BUCI008H4 Page 6 of 6 c Birkbeck College 2016

Birkbeck (University of London) Department of Computer Science and Information Systems. Introduction to Computer Systems (BUCI008H4)

Birkbeck (University of London) Department of Computer Science and Information Systems Introduction to Computer Systems (BUCI008H4) CREDIT VALUE: none Spring 2017 Mock Examination Date: Tuesday 14th March