22F_test2_keys

COMP.2030 Test 2 11/4/22 Not allowed to use electronic devices including a calculator, a cell phone, etc. ID:________________________ NAME:____________________________________________ 1. (10 pt) Variables x and y are of type integer and have arbitrary values. Variables ux and uy are unsigned values of x and y, respectively (ux = (unsigned) x; uy = (unsigned) y;). For each of the C expressions below, indicate whether the expression always yields True. Otherwise, give a reason(s) that it results in False. 1. (ux-uy) == -(unsigned)(y-x) True: Both sides are unsigned, and identical 2. ((x>>2)<<2) <=x True: The last two bits of x are zeroed out 2. (15 pt) Consider an IEEE floating point format with 4-bit exponent and 8-bit fraction (no sign bit). Show the values of the following IEEE floating point representations in binary scientific notations (1.1x2 -3 , for example) (the first four bits are exponent bits). 1000 01010000 – 1.0101x2 0000 01010000 – 0.0101x2 -6 or 1.01x2 -8 0001 01010000 – 1.0101x2 -6 3. (10 pt) Function ff() is compiled into MIPS codes on the right. Complete the C function below to make it equivalent to the MIPS code (C operator for xor is “^”). int ff (unsigned x) { int val = 0; while ( val != x ) { val ^ =x; x = x>>1 (or x /= 2); } return val; } # argument x in $a0 ff: li $t0,0 xx: beq $t0, $a0, yy xor $t0, $t0, $a0 sr a $a0, $a0, 1 b xx yy: jr $ra

4. (10 pt) Around 250 B.C., the Greek mathematician Archimedes proved that 223/71 <  <22/7. A single- precision floating-point approximation of  used in <math.h> of C language is 0x40490FDB. Write 22/7 in four hexadecimal digits according to a 16-bit floating point format with a sign bit , 6-bit exp , and 9-bit frac . 22/7 = 3 1 7 1/7*8 = 1 1/7 repeats Fraction: 001001001… 3 1 7 = 11.001001001.. in binary 11.001001001 = 1.1001001x2 1 E = 1; 6-bit exp = 100000 9-bit frac = 100100100 Sign bit = 0 Putting all together: 0 100 000 1 0010 0100 0x4124 5. (15 pt) The symbol table and the memory map of a segment of MIPS program are shown below right. Also shown are MIPS codes of three functions F0, F1, and F2. Consider the MIPS program below. As instructions are executed in the given sequence successively , write the value stored in $a0 when the program returns from each jalr instruction below . la $s1, Q2 lw $s2, ($s1) jalr $v1, $s2 $a0 = 2 lw $s1, 8($s1) lw $s2, ($s1) jalr $v1, $s2 $a0 = 1 lw $s1, 8($s1) lw $s2, ($s1) jalr $v1, $s2 $a0 = 2 Symbol Value Q0 0x10010000 Q1 0x1001000c Q2 0x10010018 F0 0x00400000 F1 0x00400008 F2 0x00400010 Addr Value Q0: F1 Q1 Q2 Q1: F0 Q0 Q2 Q2: F2 Q2 Q0 Address Value 0x10010000 0x00400008 0x10010004 0x1001000c 0x10010008 0x10010018 0x1001000c 0x00400000 0x10010010 0x10010000 0x10010014 0x10010018 0x10010018 0x00400010 0x1001001c 0x10010018 0x10010020 0x10010000 F0: li $a0, 0 jr $v1 F1: li $a0, 1 jr $v1 F2: li $a0, 2 jr $v1

8. (10 pt) Portions of a text and a data segment of a MIPS program are shown below. Functions FUN0 and FUN1 update $s0 and return the value, where the return value in $s0 is an integer between 1 and 6 (inclusive). (All three registers have to have correct answers to get credits. If any one of them is incorrect, you can give 0 grade.) a. When ‘b rept’ instruction is executed for the first time, what values will be in $s0, $s1 and $s2 ? $s0: ___2_______ $s1: ______Q0__ $s2: ______FUN1_ b. When ‘b rept’ instruction is executed for the first time, what values will be in $s1 and $s2 ? $s0: ____1______ $s1: ______Q1__ $s2: ______FUN0_ la $s1, Q1 li $s0, 1 rept: lw $s2, ($s1) jalr $v1, $s2 sll $s0, $s0, 2 add $s1, $s1, $s0 lw $s1, ($s1) b rept FUN0: li $s0, 1 jr $v1 FUN1: li $s0, 2 jr $v1 .data Q0: .word FUN0 .word Q1 .word Q1 .word Q1 .word Q1 .word Q1 .word Q1 Q1: .word FUN1 .word Q0 .word Q0 .word Q0 .word Q0 .word Q0 .word Q0