Question

3) Convert 1.25 decimal to 32 bit floating point format.
4) Convert the following truth table to a digital circuit consisting of
   NOT, AND, and OR gates.

   ABC  Out
   000  1
   001  1
   010  0
   011  0
   100  1
   101  0
   110  1
   111  0

5) Construct a tri-state buffer using transistors

10) What are the advantages of a large page size?

Answer 1

Converting 1.25 to binary
   Convert decimal part first, then the fractional part
   > First convert 1 to binary
   Divide 1 successively by 2 until the quotient is 0
      > 1/2 = 0, remainder is 1
   Read remainders from the bottom to top as 1
   So, 1 of decimal is 1 in binary
   > Now, Convert 0.25000000 to binary
      > Multiply 0.25000000 with 2.  Since 0.50000000 is < 1. then add 0 to result
      > Multiply 0.50000000 with 2.  Since 1.00000000 is >= 1. then add 1 to result
      > This is equal to 1, so, stop calculating
   0.25 of decimal is .01 in binary
   so, 1.25 in binary is 1.01
1.25 in simple binary => 1.01
so, 1.25 in normal binary is 1.01 => 1.01 * 2^0

single precision:
--------------------
sign bit is 0(+ve)
exp bits are (127+0=127) => 01111111
   Divide 127 successively by 2 until the quotient is 0
      > 127/2 = 63, remainder is 1
      > 63/2 = 31, remainder is 1
      > 31/2 = 15, remainder is 1
      > 15/2 = 7, remainder is 1
      > 7/2 = 3, remainder is 1
      > 3/2 = 1, remainder is 1
      > 1/2 = 0, remainder is 1
   Read remainders from the bottom to top as 1111111
   So, 127 of decimal is 1111111 in binary
frac bits are 01000000000000000000000

so, 1.25 in single-precision format is 0 01111111 01000000000000000000000
in hexadecimal it is 0x3FA00000