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A minifloat in 1 byte (8 bit) with 1 sign bit, 4 exponent bits and 3 significand bits (in short, a 1.4.3 minifloat) is demonstrated here. The exponent bias is defined as 7 to center the values around 1 to match other IEEE 754 floats [ 3 ] [ 4 ] so (for most values) the actual multiplier for exponent x is 2 x −7 .
If we choose to represent this value in signed 16-bit fixed format with 8 fraction bits, we must divide the integer product by 2 50-8 = 2 42 and round the result; which can be achieved by adding 2 41 and shifting by 42 bits. The result is 1720, representing the value 1720/2 8 = 6. 718 75, or approximately 6.719 ± 0.002.
2 2: 4 3: 8 4: 16 5: 32 6: 64 7: 128 8: 256 9: 512 10: ... 16 bits may be used for the integer and 16 for the fraction. The eight's bit is followed by the four's bit ...
For example, the specification Q3.12 describes a signed binary fixed-point number with a w = 16 bits in total, comprising the sign bit, three bits for the integer part, and 12 bits that are the fraction. That is, a 16-bit signed (two's complement) integer, that is implicitly multiplied by the scaling factor 2 −12
white circle u+25d8: 8: inverse bullet u+25d9: 10: inverse white circle ☺ u+263a: 1: white smiling face ☻ u+263b: 2: black smiling face ☼ u+263c: 15: white sun with rays ♀ u+2640: 12: female sign ♂ u+2642: 11: male sign ♠ u+2660: 6: black spade suit ♣ u+2663: 5: black club suit ♥ u+2665: 3: black heart suit ♦ u+2666: 4: black ...
𝟐 𝟑 𝟒 𝟓 𝟔 𝟕 𝟖 𝟗 𝟘 𝟙 𝟚 𝟛 𝟜 𝟝 𝟞 𝟟 U+1D7Ex 𝟠 𝟡 𝟢 𝟣 𝟤 𝟥 𝟦 𝟧 𝟨 𝟩 𝟪 𝟫 𝟬 𝟭 𝟮 𝟯 U+1D7Fx 𝟰 𝟱 𝟲 𝟳 𝟴 𝟵 𝟶 𝟷 𝟸 𝟹 𝟺 𝟻 𝟼 𝟽 𝟾 𝟿 Notes 1. ^ As of Unicode version 16.0 2. ^ Grey areas indicate non-assigned code points
Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest ... solutions for n = 2, 3, 4, 7, 19, ...
The leading 2 bits of the exponent and the leading digit (3 or 4 bits) of the significand are combined into the five bits that follow the sign bit. This is followed by a fixed-offset exponent continuation field. Finally, the significand continuation field made of 2, 5, or 11 10-bit declets, each encoding 3 decimal digits. [8]