offset binary
- representation:
- using binary representation of
0 -> 2^n - 1
to represent values from-k -> 2^n - k - 1
k
is the offset/bias
- using binary representation of
- 2’s complement is offset with
k = 2^(n - 1)
with negated most significant bit
1101 = -3 = -2^3 + 5
abcd 1101 = a*-(2^7) + b*2^6 + c*2^5 + d*2^4 +
2^3 + 5
=> -2^3 = 2^3 + a*-(2^7) + b*2^6 + c*2^5 + d*2^4 + 2^3
15112004 = 15 11 20 04 04 20 11 15
1010 * 2^(1100) → 010[1] * 2^(1101) 1010 → mantissa/Significand → right-most bit = 1 1100 → exponent 2 → base
exponent: 0 1 2 3 4 5 6 7 -3 -2 -1 0 1 2 3 4
0 010 10 s: 0 → + e: 010 → 2 → 2 - bias = -1 f: 10 → 1.10 (normalized has an implicit leading 1) → 1.5 (= 2^0 + 2^-1) ⇒ 1.5 * 2^-1 = 0.75