# What is exponent of denormalized real in IEEE 754 floating point format?

Here I noticed that, in table titles "Float Values (b = bias)", in exponent column, entry for denormalized reals is $00..00$, but in value column, the entry is $-b+1$. Why is there $+1$? If we consider bias of $127$ for single precision format, shouldnt it be $0-127$ only? If its $-126$, then shouldnt the entry in the exponent column be $00..01$?

(The article seems to have taken from Stallings book specified in the references. Stallings book also says the same as above.)

• (...continued) (3) You said "Since the exponent remains the same", but in 0x007fffff, exponent is 1 as can be seen here, removing bias gives $1-127 = -126$. In 0x00800000, exponent is 0 as can be seen here, which is $0-127=-127$, but is given as $-126$ only, in this table also which is precisely doubt. How they have made $0-127=-126$. (Also having other doubts, but I guess they will get cleared once I get above clarified) – anir Jan 10 '18 at 7:47