If normalized numbers are not required, the size can be reduced to 3-bit by reducing the exponent down to 1.
ɪf nˈoːɹməlˌaɪzd nˈʌmbɚz ɑːɹ nˌɑːt ɹᵻkwˈaɪɚd, ðə sˈaɪz kæn biː ɹᵻdˈuːst tə θɹˈiːbˈɪt baɪ ɹᵻdˈuːsɪŋ ðɪ ɛkspˈoʊnənt dˌaʊn tə wˈʌn.