Answer
The common value is -126, and the patterns are in the following notations:
- 10000010: Excess notation
- 01101000: Two's complement
- 00000010: Two's complement
Work Step by Step
Now, let's analyze each pattern:
1. Pattern: 10000010
- Two's complement: Interpret as -0b0000010 = -2
- Excess notation: Subtract the bias (which seems to be 128) from the pattern: 0b0000010 - 128 = -126
- Floating-point format: Interpret according to the rules of the 8-bit floating-point format presented in Figure 1.24.
2. Pattern: 01101000
- Two's complement: Interpret as 0b1101000 = 104
- Excess notation: Subtract the bias: 0b1101000 - 128 = -24
- Floating-point format: Interpret according to the rules of the 8-bit floating-point format presented in Figure 1.24.
3. Pattern: 00000010
- Two's complement: Interpret as 0b0000010 = 2
- Excess notation: Subtract the bias: 0b0000010 - 128 = -126
- Floating-point format: Interpret according to the rules of the 8-bit floating-point format presented in Figure 1.24.
Comparing the values obtained from each interpretation, we can see that the common value is -126. Now, examining the interpretations, we can conclude that:
- Pattern 10000010 corresponds to excess notation.
- Pattern 01101000 corresponds to two's complement.
- Pattern 00000010 corresponds to two's complement.
Therefore, the common value is -126, and the patterns are in the following notations:
- 10000010: Excess notation
- 01101000: Two's complement
- 00000010: Two's complement
