Range Formula
-2N-1 to +2N-1 - 1
3-bit
-4 to +3
4-bit
-8 to +7
5-bit
-16 to +15
MSB is the Sign Bit
Most significant bit indicates sign: 0 = positive, 1 = negative
Asymmetric Range
One more negative than positive (e.g., -128 to +127 for 8-bit)
Sign Extension Preserves Value
Copying sign bit when widening maintains the same value
Two's Complement Representations
| Decimal | 3-bit | 4-bit | 5-bit |
|---|
Sign Extension Demonstration
Extending -3: Copy sign bit (1) to new positions
101
→
1101
→
11101
= -3
Extending +3: Copy sign bit (0) to new positions
011
→
0011
→
00011
= +3
Key Insight: Copy the Sign Bit
Sign extension preserves value by replicating the MSB into new high-order positions