ECS50-L2

📗 -> Lecture Date: Name

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Lecture Slides

🎤 Vocab

Bit - 1 binary unit
Byte - 8 bits
Nibble - 4 bits, a small ‘byte’. Haha

❗ Unit and Larger Context

✒️ -> Scratch Notes

Working with bits:

• and, or, not, xor, left shift, arithmetic right shift, and logical right shfit
• They are performed on a per-bit basis

not	~	~A	0011
and	&	A & B	1000
or	|	A | B	1110
xor	^	A ^ B	0110
if A = 1100, B = 1010

Left Shift - A << N:

• Move the bits in A to the left by N
• Overflowing bits on left are discarded, nonexistent bits on the right are 0
• A = 10110, A << 2 = 11000
• Can be interpreted as
  • Think about how the binary representation is artificially growing by a base of 2 to the right
  • Base 10:

Logical Right Shift - A >> N:

• Move the bits in A to the right by N
• Bits that can’t fit into the result are discarded
• 0’s are brought in to fill the missing bits
  • A = 10110, A >> 2 = 00101
• Can be interpreted as

Arithmetic Right Shift - A >> N:

• Move the bits in A to the right by N
• Bits that can’t fit into the result are discarded
• Most significant bit is brought in to fill the missing bits
• Can be interpreted as

How are logical and arithmetic right shift differentiated?

Its similar to operator overloading:

• Logical right shifts are performed on unsigned variables
  • Unsigned int, unsigned short, unsigned char, …
• Arithmetic right shifts are performed on signed variables
  • Int, short, char
• The compiler actually picks different machine instructions to use based on the type

Type	A	N	Result
Left	1101 0001	3	1000 1000
Left	1101 0001	4	0001 0000
Logical Right	1101 0001	4	0000 1101
Logical Right	1101 0001	2	0011 0100
Arithmetic Right	1101 0001	4	1111 1101
Arithmetic Right	0101 0001	4	0000 0101
Can also shift by binary patterns:
0b1101 << 0b10 13 << 2 = 52 = 110100

Its STILL all bits!

void test {
	unsigned int x = -1; //0b11111111
	int x = -1; //0b11111111
 
	// 0b01111111 != 0b11111111
	assert( (x >> 1) != (y >> 1) ); 
	// Not equal because right shift happened differenly bcz of type 
 
	printf("%d", x); 
	// printing digit, outputs -1
	printf("%u", x);
	// printing unsigned int, outputs big int
 
	printf("%d", y); 
	// printing digit, outputs -1
	printf("%u", y);
	// printing unsigned int, outputs big int
 
	// Despite first assertion false, underlying bits are still the same!
}

🧪-> Example

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