Last updated April 10, 2022

Status: Tags: #aCards/cmpt295/binary Links: Binary

Binary rounding rules

Principles

• Worth of a bit is the value of 2x where x is associated with its position in the bit pattern, even though the bit itself may be 0

Types

Identify bit at rounding position, and determine rounding type:

Round up

?

• sum of bits to right > half of rounding bit
  • ex) if rounding pos is worth 1/4, check if left is greater than 1/8
  • ex) 0110 is round up
• Add 1 to the bit at rounding position, discard bits to the right

Round down

?

• sum of bits to right < half of rounding bit
  • ex) 0011 is round down
• DIscard bits

Round to even number

?

• If bits to right == bit at rounding
  • ex) 001 is round to even
• round such that the bit at the rounding position becomes 0
• If the bit at rounding position is 1 => then we round to even number by rounding up
  • Add 1 to left of position bit
• if the bit at rounding position is already 0 => then we round to even number by rounding down

Rounding IEEE

• Positioned bit is 23rd bit

Examples

Round ?

Backlinks

1

list from Binary rounding rules AND !outgoing(Binary rounding rules)

References:

Created:: 2022-01-24 14:47