The smallest possible float size that follows all IEEE principles, including normalized numbers, subnormal numbers, signed zero, signed infinity, and multiple NaN values, is a 4-bit float with 1-bit sign, 2-bit exponent, and 1-bit mantissa.
ðə smˈɔːlɪst pˈɑːsᵻbəl flˈoʊt sˈaɪz ðæt fˈɑːloʊz ˈɔːl ˌaɪˌiːˌiːˈiː pɹˈɪnsɪpəlz, ɪŋklˈuːdɪŋ nˈoːɹməlˌaɪzd nˈʌmbɚz, sˈʌbnoːɹməl nˈʌmbɚz, sˈaɪnd zˈiəɹoʊ, sˈaɪnd ɪnfˈɪnᵻɾi, ænd mˌʌltɪpəl nˈɑː ˈɛn vˈæljuːz, ɪz ɐ fˈoːɹbˈɪt flˈoʊt wɪð wˈʌnbˈɪt sˈaɪn, tˈuːbˈɪt ɛkspˈoʊnənt, ænd wˈʌnbˈɪt mæntˈɪsə.