Question

2. a) What decimal number does the bit pattern 0×0C000000 represent if it is a two’s complement integer? An unsigned integer? b) What decimal number does the bit pattern 0×0C000000 represent if it is a floating point number? Use the IEEE 754 standard. c) If the bit pattern 0×0C000000 is placed into the Instruction Register, what MIPS instruction will be executed?

Answer 1

2)
a)
Hexadecimal     Binary
    0           0000
    1           0001
    2           0010
    3           0011
    4           0100
    5           0101
    6           0110
    7           0111
    8           1000
    9           1001
    A           1010
    B           1011
    C           1100
    D           1101
    E           1110
    F           1111
Use this table to convert from hexadecimal to binary
Converting 0C000000 to binary
0 => 0000
C => 1100
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
So, in binary 0C000000 is 00001100000000000000000000000000

since left most bit is 0, this number is positive
so, we can directly convert this into a decimal value
=> 1100000000000000000000000000
=> 1x2^27+1x2^26+0x2^25+0x2^24+0x2^23+0x2^22+0x2^21+0x2^20+0x2^19+0x2^18+0x2^17+0x2^16+0x2^15+0x2^14+0x2^13+0x2^12+0x2^11+0x2^10+0x2^9+0x2^8+0x2^7+0x2^6+0x2^5+0x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 1x134217728+1x67108864+0x33554432+0x16777216+0x8388608+0x4194304+0x2097152+0x1048576+0x524288+0x262144+0x131072+0x65536+0x32768+0x16384+0x8192+0x4096+0x2048+0x1024+0x512+0x256+0x128+0x64+0x32+0x16+0x8+0x4+0x2+0x1
=> 134217728+67108864+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0+0
=> 201326592
Answer in two's complement is 201326592
Answer in unsigned is also 201326592

b)
Hexadecimal     Binary
    0           0000
    1           0001
    2           0010
    3           0011
    4           0100
    5           0101
    6           0110
    7           0111
    8           1000
    9           1001
    A           1010
    B           1011
    C           1100
    D           1101
    E           1110
    F           1111
Use this table to convert from hexadecimal to binary
Converting 0C000000 to binary
0 => 0000
C => 1100
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
0 => 0000
So, in binary 0C000000 is 00001100000000000000000000000000
00001100000000000000000000000000
0 00011000 00000000000000000000000
sign bit is 0(+ve)
exp bits are 00011000
   => 00011000
   => 0x2^7+0x2^6+0x2^5+1x2^4+1x2^3+0x2^2+0x2^1+0x2^0
   => 0x128+0x64+0x32+1x16+1x8+0x4+0x2+0x1
   => 0+0+0+16+8+0+0+0
   => 24
in decimal it is 24
so, exponent/bias is 24-127 = -103
frac bits are

IEEE-754 Decimal value is 1.frac * 2^exponent
IEEE-754 Decimal value is 1. * 2^-103
1. in decimal is 1
   => 1.
   => 1x2^0
   => 1x1
   => 1
   => 1
so, 1 * 2^-103 in decimal is 9.860761315262648e-32
so, 00001100000000000000000000000000 in IEEE-754 single precision format is 9.860761315262648e-32
Answer: 9.860761315262648e-32

c)
000011 00000000000000000000000000
opcode is 000011 (3). so, this is a jal instruction
MIPS instruction is jal 0
Answer: jal 0