the significand and exponent
Take scientific notation apart: in 6.022 * 10^23, the 6.022 is the part that carries the digits and the 23 is the part that says how big the number is. A floating-point number splits in exactly this way. The significand (often loosely called the mantissa) holds the significant digits, and the exponent is the power of the base that scales them. Value = ±significand * base^exponent. The sign is a third, separate piece, just one bit.
Inside the bits, the significand and exponent get fixed-width fields. In binary, a normalized significand is written 1.f, where the leading 1 is taken for granted and not stored — the 'implicit leading bit' — so for free you gain one extra bit of precision; only the fraction f is kept. The exponent is stored with a BIAS: instead of using a signed integer, you store exponent + bias as an unsigned number, so the smallest exponent maps to 0 and the largest to all-ones. This stored-plus-bias trick lets the same unsigned comparison hardware order floating-point magnitudes correctly.
The split is what gives floating-point its character. The significand fixes how many significant digits you carry — your RELATIVE precision, the same near 1 as near a trillion — while the exponent fixes the RANGE, how large or small a magnitude you can name. More significand bits buy precision; more exponent bits buy dynamic range. Single and double precision are simply different budgets for these two fields.
An IEEE single (32-bit) lays out 1 sign bit, 8 exponent bits, and 23 fraction bits with bias 127. To store -1.5 = -1.1 in binary * 2^0: sign = 1, fraction = 1000...0 (the 1. is implicit), and stored exponent = 0 + 127 = 127. The 24 effective significand bits give about 7 decimal significant digits.
Sign + significand + biased exponent: the three fields of a float.
'Mantissa' is the historical word but it strictly means the fractional part of a logarithm; numerical analysts prefer 'significand'. The implicit leading 1 only applies to NORMALIZED numbers — subnormals drop it.