Rounding

When converting or quantizing numbers (like converting a high-precision Fix_18_17 signal down to Fix_8_7 in FPGA design, or floating-point rounding), rounding modes define how you resolve values that fall between two integers or quantum steps.The main difference between these modes lies in how they handle exact midpoints (like $1.5$ or $-1.5$) and whether they introduce a DC bias.

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Value, Round to Even, Round to Odd, Round to Zero, Round to +∞, Round Half Up, Round Half Down +1.4, +1, +1, +1, +2 (if ceiling) / +1, +1, +1

+1.5, +2,+1,+1,+2,+2,+1

+2.5, +2,+3,+2,+3,+3,+2

−1.5, −2,−1,−1,−1,−1,−2

−2.5, −2,−3,−2,−2,−2,−3

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