1. Section A a) Find a sum of products expression for the function / given by the circuit in Figure 1 using the 8-to-1 m

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1. Section A a) Find a sum of products expression for the function / given by the circuit in Figure 1 using the 8-to-1 multiplexer. (No simplification required.) 3 1 000 z 001 0 010 -1011 0-100 1 101 z' 110 1 111 ANONON f w x y Figure 1 b) Design a circuit for the following expressions using a BCD to decimal decoder and two OR gates. You need to first decide the least and most significant bits of input (indicate these on your diagram.) 6 fi = a'd' +a.b'. 12 = a'b'.c'd' + b c d' 6 c) Decompose the following function into 4 functions for e'd', e'd, ed' and ed. g(e,d,c, b,a) = c. b +e.b.ā + d.c.b + d.c.b.a Question 1 continues overleaf.

7 Question 1 continued. d) An ASM chart for a finite state machine is shown in Figure 2. Construct a state transition table using the one hot state representation. (The code for each state is shown on the top right of the state box.) 0001 OUT 1 R 0010 T F х X OUT 2 х T F OUT 2 S 0100 1000 T х OUT 1 F Figure 2 3 e) For the ASM chart shown in Figure 2, design simplified Boolean equations for the outputs and next state logic, assuming D-type flip flops are used. A circuit diagram is not required. Total 25

2 a) Use the Quine-McCluskey method to minimise the following Boolean expression: f(a,b,c,d,e) = m(1,12,17,23) + Ed(2,4,6,14,31 ) 10 Where m represents the minterms for which must be true and the terms following d are "don't care”. The least significant bit is e. Your solution should include: 1) The detailed procedure to determine the Prime Implicants. ii) The Prime Implicant chart used for the potential elimination of some of the Prime Implicants. iii) A list of the essential Prime Implicants and the final Boolean minimum sum of products expression. 3 2 10 b) Find the minimum sum of products expression for the function G given by the following Karnaugh map (Figure 3) with map entered variables E and F. ab cd 00 00 01 11 10 1 1 Х 01 E XF 11 E 1 1 10 | XX1 G Figure 3 Total 25

Section B 3. a) Explain the following address modes: immediate addressing, register addressing and indirect addressing. 8 ró: b) Assume that the following registers initially hold the values given: r3: 0x0310F027 14: OxE3D62F27 rS: Ox3B51048D OxA0913C29 17: 0x9A404A07 Find the values held in registers rl, 12, 13 and r4 after the following ARM Cortex MO instructions are executed? i) SUBSrl, r6, 17 ii) ORRS 12,6, r5 iii) ADDS 13, 13, 15 iv) REV 4,16 c) Find the 32 bit two's complement format for the decimal numbers-12510 and -1,251,251,251,0. (Note that Ox4A949433 is the hexadecimal equivalent of +1,251,251,25110.) d) Find the IEEE 754 floating point format (single precision) for the decimal numbers, -125.510 and +12.310. 3 e) Find the decimal number that is equivalent to OxC2200000 in the IEEE754 floating point format. Total 25

4. a) The ARM Cortex MO microprocessor has four flags, namely N (negative), Z (zero), C (carry) and V (overflow). Explain what each of these flags would indicate if it was set. b) What is the state of the flags after the execution of the instruction: ADDS r2, r5, #0x001F4000 ; add 2,048,000 to r5, put sum in r4 i) when the value held by r5 is 0x00E0B000 ii) when the value held by r5 is 0x800F4000 iii) when the value held by r5 is 0xFFE0C000 c) The carry flag can be used in two different ways; explain both uses of the carry flag. 3 d) Demonstrate how the carry flag can be used to add two positive integers if the integers are greater than 4.3x10'e.g. 6x10° +6x10' (Ox0000000D F8475800 + 0x0000008B B2C97000) Total 25