Bit Manipulation Basics AND OR XOR NOT Left Right Shift in DSA C - Execution Trace

Concept Flow - Bit Manipulation Basics AND OR XOR NOT Left Right Shift

Start with two numbers

↓

Apply AND (&)

→Result: bits set only if both bits are 1

↓

Apply OR (|)

→Result: bits set if either bit is 1

↓

Apply XOR (^)

→Result: bits set if bits differ

↓

Apply NOT (~)

→Result: bits flipped

↓

Apply Left Shift (<<)

→Result: bits shifted left, zeros fill right

↓

Apply Right Shift (>>)

→Result: bits shifted right, sign bit or zero fill

↓

End

Start with two numbers, then apply each bitwise operation step-by-step to see how bits change.

Execution Sample

DSA C

int a = 6;  // 00000110
int b = 11; // 00001011
int c;
c = a & b;
c = a | b;
c = a ^ b;
c = ~a;
c = a << 1;
c = b >> 2;

This code applies AND, OR, XOR, NOT, left shift, and right shift on two numbers and stores results.

Execution Table

Step	Operation	Input Values (a, b)	Result (decimal)	Result (binary)	Explanation
1	AND (&)	a=6 (00000110), b=11 (00001011)	2	00000010	Bits set only where both a and b have 1
2	OR (|)	a=6 (00000110), b=11 (00001011)	15	00001111	Bits set where either a or b has 1
3	XOR (^)	a=6 (00000110), b=11 (00001011)	13	00001101	Bits set where a and b bits differ
4	NOT (~)	a=6 (00000110)	-7	11111001 (2's complement)	Bits flipped; in 8-bit signed, ~6 = -7
5	Left Shift (<< 1)	a=6 (00000110)	12	00001100	Bits shifted left by 1, zero fills right
6	Right Shift (>> 2)	b=11 (00001011)	2	00000010	Bits shifted right by 2, zeros fill left
7	End	-	-	-	All operations completed

💡 All bitwise operations applied to inputs; execution ends.

Variable Tracker

Variable	Initial	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	Final
a	6 (00000110)	6	6	6	6	6	6	6
b	11 (00001011)	11	11	11	11	11	11	11
c	undefined	2 (00000010)	15 (00001111)	13 (00001101)	-7 (11111001)	12 (00001100)	2 (00000010)	2

Key Moments - 3 Insights

Why does NOT (~) of 6 give -7 instead of a positive number?

Because NOT flips all bits including the sign bit in two's complement representation, resulting in a negative number as shown in step 4 of the execution_table.

Why does left shift (<<) multiply the number by 2?

Left shift moves bits to the left, adding a zero on the right, effectively doubling the number as seen in step 5 where 6 becomes 12.

What happens to bits shifted out in right shift (>>)?

Bits shifted out on the right are discarded, and zeros fill in from the left for unsigned or positive numbers, as shown in step 6 where 11 >> 2 becomes 2.

Visual Quiz - 3 Questions

Look at the execution_table at step 3, what is the binary result of a ^ b?

A 00001101

B 00001111

C 00000010

D 11111001

💡 Hint

Check the 'Result (binary)' column at step 3 in execution_table.

At which step does the variable c become negative?

A Step 5

B Step 2

C Step 4

D Step 6

💡 Hint

Look at the 'Result (decimal)' column for negative values in execution_table.

If we change a to 3 (00000011), what would be the result of a & b at step 1?

A 2

B 3

C 1

D 0

💡 Hint

AND sets bits only where both inputs have 1; compare bits of 3 and 11.

Concept Snapshot

Bit Manipulation Basics:
- AND (&): bits set if both bits 1
- OR (|): bits set if either bit 1
- XOR (^): bits set if bits differ
- NOT (~): bits flipped (two's complement)
- Left Shift (<<): bits shift left, zero fill right
- Right Shift (>>): bits shift right, zero or sign fill left

Full Transcript

This lesson shows how to use basic bit manipulation operators in C. We start with two numbers, 6 and 11, and apply AND, OR, XOR, NOT, left shift, and right shift. Each operation changes bits in a specific way. AND keeps bits set only if both inputs have 1. OR sets bits if either input has 1. XOR sets bits where inputs differ. NOT flips all bits, which can produce negative numbers in two's complement. Left shift moves bits left, doubling the number. Right shift moves bits right, dividing by powers of two. The execution table traces each step with decimal and binary results. Variable tracking shows how values change. Key moments clarify common confusions about negative results and bit shifts. Visual quizzes test understanding by referencing the execution steps and bit patterns.