CPU status flag behavior

The flags register, also called processor status or just P, is one of the six architectural registers on the 6502 family CPU.

There are six bits in P:

7654 3210
||   ||||
||   |||+- C: 1 if last addition or shift resulted in a carry, or if
||   |||   last subtraction resulted in 
||   ||+-- Z: 1 if last operation resulted in a 0 value
||   |+--- I: Interrupt priority level
||   |     (0: /IRQ and /NMI get through; 1: only /NMI gets through)
||   +---- D: 1 to make ADC and SBC use binary-coded decimal arithmetic
||         (ignored on second-source 6502 like that in the NES)
|+-------- V: 1 if last ADC or SBC resulted in signed overflow, or
|          D6 from last BIT read as 0
+--------- N: Set to bit 7 of the last operation

The B flag

There is no "B flag". Bits 5 and 4 of flags do not exist.

Two signals and two instructions can push flags to the stack. When they do so, they fill the unused bits with the following:

Instruction	Bits 5 and 4	Side effects after pushing
PHP	11	None
BRK	11	I is set to 1
/IRQ	10	I is set to 1
/NMI	10	I is set to 1

Two instructions (PLP and RTI) pull a byte from the stack and set flags, but they ignore bits 5 and 4.