The Z80's bitlevel instructions enable you to manipulate the individual bits of registers and bytes in memory. You must be familiar with binary notation to continue. If you need some review, look back to Day 3.
Bit Logic Instructions
There are four main logical (a.k.a boolean) operations, called AND, OR, XOR, and NOT. All except NOT are dyadic (they want two operands). To figure out what the result of a dyadic logical operation is, the values of the two operands must be worked on in binary. The operator is applied to a bit in one value and the corresponding bit in the other value; this is done for each bit. The result of each operator can be found by consulting this table:
bit 1  bit 2  AND  OR  XOR  NOT 

0 
0 
0 
0 
0 
1 
0 
1 
0 
1 
1 

1 
0 
0 
1 
1 
0 
1 
1 
1 
1 
0 
Examples:
%11110000 AND %01010101 %01010000
%11110000 OR %01010101 %11110101
%11110000 XOR %01010101 %10100101
NOT %11110000 %00001111
Naturally, the logical operations are available as Z80 instructions.
AND {reg8  imm8  (HL) }
Bitwise AND on the accumulator.
 S
 affected
 Z
 affected
 P/V
 detects parity
 C
 reset
OR {reg8  imm8  (HL) }
Bitwise OR on the accumulator.
 S
 affected
 Z
 affected
 P/V
 detects parity
 C
 reset
XOR {reg8  imm8  (HL) }
Bitwise exclusive OR on the accumulator.
 S
 affected
 Z
 affected
 P/V
 detects parity
 C
 reset
CPL
 Bitwise complement (NOT) of the accumulator.
Bit Masking
The boolean operations are mainly used in a technique called "bit masking", which allows you to set or reset specific bits.
Setting Bits
To set bits, use OR. For the mask, use 1 for each bit you want forced to be set, and 0 for the bits you want to preserve. Typically, you would use an OR bitmask to integrate some pattern into a byte without disturbing the other bits.
E.g. Use OR to force bits 1, 4, 5, and 7 to be set.
%00000000 %01100101 %10001111 OR %10110010 OR %10110010 OR %10110010 %10110010 %11110111 %10111111
Resetting Bits
To reset bits, use AND. For the mask, use 0 for each bit to reset, and 1 for each bit to ignore. Use this AND bitmask to remove bits that are considered "garbage" from a piece of data.
E.g. Use AND to force bits 0, 1, 2, and 6 to be reset.
%11111111 %00111001 %01101101 AND %10111000 AND %10111000 AND %10111000 %10111000 %00111000 %00101000
Toggling Bits
To flip the state of a bit, use XOR. For the mask, use 1 for each bit to flip, and 0 for each bit to ignore.
E.g. Use XOR to flip bits 7 to 4.
%10101010 %11001100 %01011110 XOR %11110000 XOR %11110000 XOR %11110000 %01011010 %00111100 %10101110
Uses For Bitmasking
16Bit Counters
Because the only way to get a result of zero with an OR operation is when both operands are zero, it can be used when you want a 16bit counter.
Loop: DEC BC ; Update the counter LD A, B ; Load one half of the counter OR C ; Bitmask with the other half of the counter JR NZ, Loop ; If Z is reset then neither B or C is zero, so repeat
Calculating Remainders
AND can be used to perform modulo with a power of two.
AND %00011111 ; A = A mod 32 AND %00000111 ; A = A mod 8
ModuloN Counters
This feature of AND can be used to implement a modulon counter. The premise is that a value is incremented until it hits 2^{n}, at which point it resets to zero. Think of it as a clock with 2^{n} digits. The format for such a counter is:
Loop: LD A, (count) INC A AND 2^n1 LD (count), A JP Z, Fishkill JR Loop
Optimizing
Some cheap optimization tricks with boolean operations.
Instruction  Bytes  Cycles  Replacement  Bytes  Cycles  Downside 

CP 0 
2  7  OR A / AND A 
1  4  P/V flag is affected differently 
LD A, 0 
2  7  XOR A 
1  4  Flags are affected.SUB A will have the same effect, btw 
Signed Comparisons
If you remember, when subtracting one signed number from another, we can tell how the two numbers compare based on the sign and overflow flags:
Sign  Overflow  Meaning 

SET  SET  op1 >= op2 
SET  CLEAR  op1 < op2 
CLEAR  SET  op1 < op2 
CLEAR  CLEAR  op1 >= op2 
Interestingly, this looks just like the operation of XOR. So one could surmise that XORing the sign and overflow flags together after a comparison would yield their relationship.
Now, while it is impossible to do an operation on two flag bits, we can take advantage of the fact that the sign bit is a copy of the seventh bit of the result, then use an XOR bitmask if it's warranted. Although, this means that you have to use SUB instead of CP to do the comparison.
SUB 5 JP PO, $+5 ; P/V reset, and XORing with zero does nothing XOR $80 ; Can now use M for <, or P for >=
Be aware that this method does not leave the Z flag in any meaningful state.
SingleBit Instructions
SET n, {reg8  (HL) }
 Sets bit
n
(07) of the operand. RES n, {reg8  (HL) }
 Resets bit
n
(07) of the operand. BIT n, {reg8  (HL) }
Checks bit
n
(07) of the operand. S
 not affected
 Z
 affected
 P/V
 not affected
 C
 not affected
These instructions can be useful, because they allow you to do bitmasking without having to involve the accumulator.
There is a feature of the TIOS called the system flags that you can take advantage of with these instructions. For starters, look at the Mode or Format menu. You'll see a bunch of options that affect graphing, trigonometry, numbers, etc. Each of these options is controlled by a system flag.
Register IY
IX has a sister register called IY that is entirely interchangeable with its dÃ¶ppelganger, but the OS has called dibs on it.
All the system flags are in an array with a base at $89F0, and the calculator has this address stored in IY. We can modify a system flag with the SET/RES instructions, and check them with the BIT instruction.
Example: This will check the trigonometric mode. If this bit is 1, then degree mode is set. If it's 0, radian mode is set.
BIT 2, (IY + 0) ; Checks bit 2 of byte $89F0
What relates 2 and 0 to with trigonometry? Not much, the fact that this bit and byte combination record the trig setting was a completely arbitrary decision on TI's part. That's why all the bytes and offsets of the system flags are equated in the INC file:
BIT TrigDeg, (IY + TrigFlags)
TrigDeg is equal to 2, and TrigFlags is equal to 0. This will do the same thing as above, but it's a lot easier to understand.