4.14) Meaning of bits patterns:

1000 1111 1110 1111 1100 0000 0000 0000₂

a) a two's complement integer?

1) Notice leading bit is 1 which mean negative number

    => sign = negative

2) invert bits

        0111 0000 0001 0000 0011 1111 1111 1111

3)    Add the invert to 1

        0111 0000 0001 0000 0011 1111 1111 1111

                                                                          + 1

        0111 0000 0001 0000 0100 0000 0000 0000

4) Convert two's complement bit to decimal

        0111 0000 0001 0000 0100 0000 0000 0000₂

          2³⁰ + 2²⁹ + 2²⁸ + 2²⁰ + 2¹⁴ = 1,880,113,152

5) Add sign to the decimal number

    sing = negative

    => - 1,880,113,152

b)    An unsigned number?

        For the  unsigned number, we use maximum bit pattern.

        MIPS word is 32 bits long = 2³² = 4,294,967,295₁₀

Unsigned number binary conversion to decimal:

                                         1000  1111  1110  1111  1100  0000  0000  0000₂

2³¹ + 2²⁷ + 2²⁶ + 2²⁵ + 2²⁴ + 2²³ + 2²² + 2²¹ + 2¹⁹ + 2¹⁸ + 2¹⁷ + 2¹⁶ + 2¹⁵ + 2¹⁴ = 2,414,854,144

c)    A single precision floating-point number)

        S = 1

        E = 0001 1111 = 31₁₀

           Significant =  .1101 1111 1000 = 1/2 + 1/4 + 0/8 +1/16 + 1/32 + 1/64 +1/128 + 1/256 +1/512

                        = .873046875

        IEEE 754 format: (-1)^S x (1 + Significant) x 2^{(Exponent - Bias)}

        = (-1)¹ x (1 + .873046875) x 2^{(31 - 127)}

        = -1 x 1.873046875 x 2^-96

        = - 1.873046875 x 1.262177448 x 10^-29

        = - 2.364117525 x 10^-29

d)    a MIPS instruction)

OP = 10 0011 = 35₁₀

=> OP35 = lw

RS = 1 1111 = 31₁₀ = $ra  (page 140)

RT = 0 1111 = 15₁₀ = $t7

address/ imediate = 1100 0000 0000 0000 = 4952₁₀

=> MIPS instruction is: lw $t7, 49152($ra)