When possible, SHOW YOUR WORK.

1.  What is the largest positive and smallest negative numbers possible in:

a.  5-bit 2's complement notation

largest positive = 01111 = +15
smallest negative = 10000 = -16

b.  7-bit 2's complement notation

largest positive = 0111111 = +63
smallest negative = 1000000 = -64

a) Sign bit = 1 (this is negative)
b) 71 = 64 + 4 + 2 + 1 = 1000111₂
c) 0.34375 = 1/4 + 1/16 + 1/32 = 0.01011₂
d) 71.034375 = 1000111.01011₂ = 1.00011101011₂  x 2⁶
e) exponent+127 = 133 = 128 + 4 + 1 = 10000101₂
g) [sign,exp+127,mantissa-san-leading-1] = 1 10000101 00011101011₂
h) g with proper spacing and trailing 0's = 1100 0010 1000 1110 1011 0000 0000 0000₂

a.  Express it in base 10

0x4162 = (256 * (4 * 16 + 1))   +   (6 * 16 + 2)  = (256 * 65) + 98 = 16,738

b.  Express it in binary (base 2)

  4    1    6    2
0100 0001 0110 0010₂

c.  Assuming this is ASCII, what characters does it represent?

0x41 = 65 which is A
0x62 = 98 which is b
Thus, it is the string Ab

d.  Assuming it is a 2-byte 2's complement number, what number does it represent?

This is the same as part a: 16,738.

e.  Assuming it is a 2-byte unsigned integer, what number does it represent?

Because the high-order bit (the sign bit) is 0, this is also the same as part a:  16,738.

f.  Assuming it is a floating-point number (with trailing 0's as needed to pad to 32 bits), what number does it represent?

a) Express in base 2:  0100 0001 0110 0010₂
b) Sign bit = 0, so positive
c) Exp+127 = 10000010₂ = 128 + 2 = 130, so exp = 3
d) mantissa-sans-leading 1 = .110010₂
e) Put this together to get:  1.11001₂ * 2³ = 1110.01₂ = 8 + 4 + 2 + 1/4 = 14.25