With the configurable exponent bias set to the minimum possible value (0000002 = 0), the numerical values that can be represented in the normalized CFloat_1_4_3 format are shown below. E = 0001 − 000000 = 1; E = 1111 − 000000 = 15 min 2 2 max 2 2 The range of numerical values thus represented is 1 15 +/- [1.0002 x 2, 1.1112 x 2 ]. Similarly, with the exponent bias set to the maximum possible value (111111 = 63), 2 E = 0001 − 111111 = -62; E = 1111 − 111111 = -48 min 2 2 max 2 2 The range of numerical values thus represented is -62 -48 +/- [1.000 x 2 , 1.111 x 2 ] 2 2 For normalized floating point numbers in the CFloat8_1_4_3 format, the numerical values for exponent bias values of 0, 1, 2, 3,…, 62, 63 are shown in Table 4 below. The entire exponent range [-62, 15] can be spanned by this format by reconfiguring the exponent bias appropriately. Please note that the exponent range with a 4-bit exponent with a fixed bias only spans 15 consecutive exponent values. For example, for bias = 31, only the exponent range [-30, -16] can be spanned. Table 4: Range of numerical values of normalized floating-point numbers in CFloat8_1_4_3 format for various exponent bias values Exponent Bias Range of Numerical Values 0 +/-[1.000 x 21, 1.111 x 215] 0 14 1 +/-[1.000 x 2 , 1.111 x 2 ] -1 13 2 +/-[1.000 x 2 , 1.111 x 2 ] -2 12 3 +/-[1.000 x 2 , 1.111 x 2 ] ... 31 +/-[1.000 x 2-30, 1.111 x 2-16] ... -59 -45 60 +/-[1.000 x 2 , 1.111 x 2 ] -60 -46 61 +/-[1.000 x 2 , 1.111 x 2 ] 62 +/-[1.000 x 2-61, 1.111 x 2-47] -62 -48 63 +/-[1.000 x 2 , 1.111 x 2 ] 05 Tesla Dojo Technology — A Guide to Tesla’s Configurable Floating Point Formats & Arithmetic