quiz 5

Question 1

Adding integer rules

Answer 1

1 + 1 = 0 carry 1
1 + 0/0 + 1 = 1
0 + 0 = 0

Question 2

Bit-wise flipping syntax

Answer 2

bar on top of the number

Question 3

Signed magnitude changing the sign

Answer 3

Replace the sign bit with the opposite

Question 4

One’s complement changing the sign

Answer 4

flip everything

Question 5

Two’s complement changing the sign

Answer 5

Flip everything and add one

Question 6

Single precision length?

Answer 6

32 bits, 1 sign bit, 23 bits significand, 8 bits exponent, bias 127

Question 7

Double precision length?

Answer 7

64 bits, 1 sign bit, 52 bits significand, 11 bits exponent, bias 1023

Question 8

Quadruple precision length?

Answer 8

128 bits, 1 sign bit, 112 bits significand, 15 bits exponent, bias 16383

Question 9

Half precision length?

Answer 9

16 bits, 1 sign bit, 10 bits significand, 5 bits exponent, bias 15

Question 10

Convert decimal to IEEE 754

Answer 10

• Determine sign bit:
  o -42.625 is negative, therefore sign bit is 1.
• Convert number to binary:
  o 101010.101 x 2^0
• Shift point so that there is only one 1 in front of the point:
  o 1.01010101 x 2^5
• Add bias to the exponent value:
  o 32-bit floating point numbers, the bias is 127.
  o 5 + 127 = 132
• Convert exponent to the binary system
  o 132 = 10000100
• Assemble floating point number:
  o 1.10000100.01010101000000000000000

Question 11

Convert IEEE 754 into decimal

Answer 11

• 0.10000100.10111001000000000000000
• Convert exponent to decimal
  o 10000100 = 132
• Subtract bias from exponent
  o 132-127 = 5
• Extend mantissa by leading “1” (add a 1 to the end)
  o 1.10111001000000000000000
• Shift point
  o The binary point must be shifted so that the exponent becomes 0.
  o If the exponent is greater than 0, the point must be moved to the right, otherwise to the left
  o 110111.001000000000000000
• Convert mantissa to decimal number
  o 110111.001 = 55.125