Single-precision floating-point format Range -

sign = 1 bit, biased exponent = 8 bits, mantissa = 23 bits

what positive , negative possible range? teacher told me following range:

-0.5*2^-128 -(1-2^-24)*2^127 (for negative floating point numbers)  0.5*2^-128 (1-2^-24)*2^127 (for positive floating point numbers) 

but don't find range correct because not able understand how store 0.5 * 2^-128 format. please explain.

firstly, floating-point number format symmetric positive , negative numbers. @ positive case.

the maximum positive number has maximum mantissa 1.11111111111111111111111₂ , maximum non-infinite exponent 127. 1.11111111111111111111111₂ × 2¹²⁷ = (2 − 2⁻²³) × 2¹²⁷ ≈ 3.402 × 10³⁸ ≈ 2¹²⁸.

the minimum positive number has non-zero mantissa 0.00000000000000000000001₂ , minimum exponent −126 subnormal/denormalized numbers. 0.00000000000000000000001₂ × 2⁻¹²⁶ = 2⁻²³ × 2⁻¹²⁶ = 2⁻¹⁴⁹ ≈ 1.401 × 10⁻⁴⁵.

further reading: https://en.wikipedia.org/wiki/single-precision_floating-point_format