(h) Edge-Triggered Flip-Flop:
An edge-triggered flip-flop is a type of flip-flop that changes its state only on the edge (transition) of a clock signal. There are two types of edges: rising edge (positive edge) and falling edge (negative edge). The most common edge-triggered flip-flops are the positive edge-triggered (or simply edge-triggered) D flip-flop and the JK flip-flop. Let's use the D flip-flop as an example.
Functioning:
The edge-triggered D flip-flop changes its state (stores the value of the D input) only when the clock signal transitions from one state to another. For example, in a positive edge-triggered D flip-flop, the state changes on the rising edge of the clock signal.
Diagram:
```
+-----+
D ---->| |
| D |---- Q
CLK--->| F |
| F |---- Q'
| L |
+-----+
```
- \( D \): Data input
- \( Q \): Output
- \( Q' \): Complement of output
- \( CLK \): Clock input
(i) IEEE 754 Single Precision and Double Precision Formats:
IEEE 754 Single Precision (32 bits):
Representation of (-121.25)10:
- Sign bit (1 bit): 1 (negative)
- Exponent (8 bits): \(2^{127 - 1 + 8} = 2^{134}\)
- Mantissa (23 bits): The binary representation of the fractional part
The binary representation of 121.25 is \(1111001.01\). The normalized form is \(1.11100101 \times 2^6\).
Putting it all together:
\[ \text{Single Precision} = 1 \, | \, 10000110 \, | \, 11100101000000000000000 \]
Representation of (0.0625)10:
- Sign bit (1 bit): 0 (positive)
- Exponent (8 bits): \(2^{127 - 1 - 6} = 2^{120}\)
- Mantissa (23 bits): The binary representation of the fractional part
The binary representation of 0.0625 is \(0.0001\). The normalized form is \(1.0 \times 2^{-4}\).
Putting it all together:
\[ \text{Single Precision} = 0 \, | \, 01111010 \, | \, 00000000000000000000000 \]
IEEE 754 Double Precision (64 bits):
The format is similar to single precision but with a longer mantissa.
Representation of (-121.25)10:
\[ \text{Double Precision} = 1 \, | \, 10000000011 \, | \, 1110010100000000000000000000000000000000000000000000 \]
Representation of (0.0625)10:
\[ \text{Double Precision} = 0 \, | \, 01111111110 \, | \, 0000000000000000000000000000000000000000000000000000 \]
In both cases, the sign bit, exponent, and mantissa are formatted according to IEEE 754 standards for single and double precision.
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