Logic Micro-operations

Logic micro-operations: AND, OR, XOR, NOT operations on register contents with applications.

Introduction

While arithmetic micro-operations deal with numerical calculations, logic micro-operations perform bitwise Boolean operations on register contents. They don't treat the register as a number — instead, they operate on each bit independently. These operations are incredibly powerful for tasks like masking specific bits, setting flags, clearing fields, toggling states, and packing/unpacking data. Every programmer who's done bit manipulation is using logic micro-operations at the hardware level.

The Four Basic Logic Micro-operations

AND (∧)

Example

R1 ← R1 ∧ R2 (bitwise AND)

Each bit of the result is 1 only if BOTH corresponding input bits are 1.

R1	1 0 1 1 0 1 1 0
R2	1 1 0 1 0 0 1 1
R1	1 0 0 1 0 0 1 0

Primary use: Masking (clearing specific bits) To clear bits 4-7 while keeping bits 0-3:

Example

R1 ← R1 ∧ 00001111 ; Mask: 1s keep, 0s clear

OR (∨)

Example

R1 ← R1 ∨ R2 (bitwise OR)

Each bit of the result is 1 if EITHER (or both) input bits are 1.

R1	1 0 1 1 0 0 0 0
R2	0 0 0 0 1 1 0 1
R1	1 0 1 1 1 1 0 1

Primary use: Setting specific bits To set bits 0 and 2 without disturbing others:

Example

R1 ← R1 ∨ 00000101 ; Mask: 1s set, 0s preserve

XOR (⊕)

Example

R1 ← R1 ⊕ R2 (bitwise exclusive OR)

Each bit of the result is 1 if the input bits are DIFFERENT.

R1	1 0 1 1 0 1 1 0
R2	1 1 0 1 0 0 1 1
R1	0 1 1 0 0 1 0 1

Primary uses:

Toggling bits: XOR with 1 flips a bit; XOR with 0 preserves it
Comparing: If R1 ⊕ R2 = 0, then R1 = R2
Clearing a register: R1 ← R1 ⊕ R1 (always gives 0, faster than loading 0)
Swapping without temp: A⊕=B, B⊕=A, A⊕=B

NOT (Complement)

Example

R1 ← R̄1 (bitwise complement)

Each bit is inverted: 0→1, 1→0.

Example

R1: 1 0 1 1 0 1 1 0 ───────────────────── R1: 0 1 0 0 1 0 0 1

Primary use: One's complement, creating masks

Complete Set of Logic Micro-operations

With two input variables (per bit position), there are 2⁴ = 16 possible logic functions:

Operation	Result	Name
F = 0	Clear	Always zero
F = A ∧ B	AND	Both bits 1
F = A ∧ B̄	Inhibit	A but not B
F = A	Transfer A	Copy A
F = Ā ∧ B	Inhibit	B but not A
F = B	Transfer B	Copy B
F = A ⊕ B	XOR	Different bits
F = A ∨ B	OR	Either bit 1
F = (A ∨ B)'	NOR	Neither bit 1
F = (A ⊕ B)'	XNOR	Same bits
F = B̄	Complement B	Invert B
F = A ∨ B̄	---	A or not B
F = Ā	Complement A	Invert A
F = Ā ∨ B	---	Not A or B
F = (A ∧ B)'	NAND	Not both 1
F = 1	Set	Always one

In practice, processors implement AND, OR, XOR, and NOT — all 16 functions can be derived from these four.

Hardware Implementation

Logic Unit Circuit

A logic unit for n-bit registers consists of n identical 1-bit slices:

For each bit position i: A[i] ──┬──► AND gate ──┐ B[i] ──┤ │ ├──► OR gate ──┼──► 4-to-1 MUX ──► F[i] ├──► XOR gate ──┤ ↑ └──► NOT gate ──┘ Select (S1,S0) (of A[i])

Select lines (S1, S0) choose which operation's output reaches the result:

S1	S0	Output
0	0	A AND B
0	1	A OR B
1	0	A XOR B
1	1	NOT A

Practical Applications

Bit Masking

Extract specific bit fields from a register:

Example

; Extract bits 4-7 from R1 (shift not shown here) R2 ← R1 ∧ 11110000 ; Clear bits 0-3, keep bits 4-7

Setting Flags

Set specific control bits:

Example

; Set the "interrupt enable" bit (bit 3) in status register SR ← SR ∨ 00001000

Clearing Flags

Clear specific bits:

Example

; Clear the "carry" bit (bit 0) in status register SR ← SR ∧ 11111110

Toggling

Flip specific bits:

Example

; Toggle bit 7 (often used for LED blinking in embedded systems) PORT ← PORT ⊕ 10000000

Testing Bits

Check if a specific bit is set:

Example

TEMP ← R1 ∧ 00000100 ; Isolate bit 2 ; If TEMP = 0, bit 2 was 0; if TEMP ≠ 0, bit 2 was 1

Packing/Unpacking Data

Combine two 4-bit values into one 8-bit register:

Example

R3 ← (R1 ∧ 00001111) ∨ (shl(R2,4) ∧ 11110000)

Logic vs Arithmetic Operations

Feature	Logic Micro-ops	Arithmetic Micro-ops
Bit interaction	Each bit independent	Carries propagate between bits
Number interpretation	Bits have no numeric meaning	Bits form a number
Carry	No carry generation	Carry is essential
Speed	Faster (no carry chain)	Slightly slower (carry propagation)
Use case	Bit manipulation, masking	Mathematical computation

Key Takeaways

Logic micro-operations perform bitwise Boolean operations — each bit is processed independently
The four essential operations: AND (mask/clear), OR (set), XOR (toggle/compare), NOT (invert)
No carry propagation occurs — making logic operations inherently faster than arithmetic
AND with a mask clears bits; OR with a mask sets bits; XOR with a mask toggles bits
XOR of a register with itself clears it (R←R⊕R = 0) — the fastest way to zero a register
All 16 possible two-variable logic functions exist, but AND, OR, XOR, NOT suffice in practice
Logic and arithmetic circuits are combined in the ALU, selected by control signals

Introduction

The Four Basic Logic Micro-operations

AND (∧)

Example

R1 ← R1 ∧ R2 (bitwise AND)

Each bit of the result is 1 only if BOTH corresponding input bits are 1.

R1	1 0 1 1 0 1 1 0
R2	1 1 0 1 0 0 1 1
R1	1 0 0 1 0 0 1 0

Primary use: Masking (clearing specific bits) To clear bits 4-7 while keeping bits 0-3:

Example

R1 ← R1 ∧ 00001111 ; Mask: 1s keep, 0s clear

OR (∨)

Example

R1 ← R1 ∨ R2 (bitwise OR)

Each bit of the result is 1 if EITHER (or both) input bits are 1.

R1	1 0 1 1 0 0 0 0
R2	0 0 0 0 1 1 0 1
R1	1 0 1 1 1 1 0 1

Primary use: Setting specific bits To set bits 0 and 2 without disturbing others:

Example

R1 ← R1 ∨ 00000101 ; Mask: 1s set, 0s preserve

XOR (⊕)

Example

R1 ← R1 ⊕ R2 (bitwise exclusive OR)

Each bit of the result is 1 if the input bits are DIFFERENT.

R1	1 0 1 1 0 1 1 0
R2	1 1 0 1 0 0 1 1
R1	0 1 1 0 0 1 0 1

Primary uses:

Toggling bits: XOR with 1 flips a bit; XOR with 0 preserves it
Comparing: If R1 ⊕ R2 = 0, then R1 = R2
Clearing a register: R1 ← R1 ⊕ R1 (always gives 0, faster than loading 0)
Swapping without temp: A⊕=B, B⊕=A, A⊕=B

NOT (Complement)

Example

R1 ← R̄1 (bitwise complement)

Each bit is inverted: 0→1, 1→0.

Example

R1: 1 0 1 1 0 1 1 0 ───────────────────── R1: 0 1 0 0 1 0 0 1

Primary use: One's complement, creating masks

Complete Set of Logic Micro-operations

With two input variables (per bit position), there are 2⁴ = 16 possible logic functions:

Operation	Result	Name
F = 0	Clear	Always zero
F = A ∧ B	AND	Both bits 1
F = A ∧ B̄	Inhibit	A but not B
F = A	Transfer A	Copy A
F = Ā ∧ B	Inhibit	B but not A
F = B	Transfer B	Copy B
F = A ⊕ B	XOR	Different bits
F = A ∨ B	OR	Either bit 1
F = (A ∨ B)'	NOR	Neither bit 1
F = (A ⊕ B)'	XNOR	Same bits
F = B̄	Complement B	Invert B
F = A ∨ B̄	---	A or not B
F = Ā	Complement A	Invert A
F = Ā ∨ B	---	Not A or B
F = (A ∧ B)'	NAND	Not both 1
F = 1	Set	Always one

In practice, processors implement AND, OR, XOR, and NOT — all 16 functions can be derived from these four.

Hardware Implementation

Logic Unit Circuit

A logic unit for n-bit registers consists of n identical 1-bit slices:

Select lines (S1, S0) choose which operation's output reaches the result:

S1	S0	Output
0	0	A AND B
0	1	A OR B
1	0	A XOR B
1	1	NOT A

Practical Applications

Bit Masking

Extract specific bit fields from a register:

Example

; Extract bits 4-7 from R1 (shift not shown here) R2 ← R1 ∧ 11110000 ; Clear bits 0-3, keep bits 4-7

Setting Flags

Set specific control bits:

Example

; Set the "interrupt enable" bit (bit 3) in status register SR ← SR ∨ 00001000

Clearing Flags

Clear specific bits:

Example

; Clear the "carry" bit (bit 0) in status register SR ← SR ∧ 11111110

Toggling

Flip specific bits:

Example

; Toggle bit 7 (often used for LED blinking in embedded systems) PORT ← PORT ⊕ 10000000

Testing Bits

Check if a specific bit is set:

Example

TEMP ← R1 ∧ 00000100 ; Isolate bit 2 ; If TEMP = 0, bit 2 was 0; if TEMP ≠ 0, bit 2 was 1

Packing/Unpacking Data

Combine two 4-bit values into one 8-bit register:

Example

R3 ← (R1 ∧ 00001111) ∨ (shl(R2,4) ∧ 11110000)

Logic vs Arithmetic Operations

Feature	Logic Micro-ops	Arithmetic Micro-ops
Bit interaction	Each bit independent	Carries propagate between bits
Number interpretation	Bits have no numeric meaning	Bits form a number
Carry	No carry generation	Carry is essential
Speed	Faster (no carry chain)	Slightly slower (carry propagation)
Use case	Bit manipulation, masking	Mathematical computation

Key Takeaways

Logic micro-operations perform bitwise Boolean operations — each bit is processed independently
The four essential operations: AND (mask/clear), OR (set), XOR (toggle/compare), NOT (invert)
No carry propagation occurs — making logic operations inherently faster than arithmetic
AND with a mask clears bits; OR with a mask sets bits; XOR with a mask toggles bits
XOR of a register with itself clears it (R←R⊕R = 0) — the fastest way to zero a register
All 16 possible two-variable logic functions exist, but AND, OR, XOR, NOT suffice in practice
Logic and arithmetic circuits are combined in the ALU, selected by control signals

Logic Micro-operations

Introduction

The Four Basic Logic Micro-operations

AND (∧)

OR (∨)

XOR (⊕)

NOT (Complement)

Complete Set of Logic Micro-operations

Hardware Implementation

Logic Unit Circuit

Practical Applications

Bit Masking

Setting Flags

Clearing Flags

Toggling

Testing Bits

Packing/Unpacking Data

Logic vs Arithmetic Operations

Key Takeaways

Continue learning this concept

Logic Micro-operations

Introduction

The Four Basic Logic Micro-operations

AND (∧)

OR (∨)

XOR (⊕)

NOT (Complement)

Complete Set of Logic Micro-operations

Hardware Implementation

Logic Unit Circuit

Practical Applications

Bit Masking

Setting Flags

Clearing Flags

Toggling

Testing Bits

Packing/Unpacking Data

Logic vs Arithmetic Operations

Key Takeaways

Continue learning this concept