Answer:Introduction:
Binary subtractors are used in digital circuits to perform arithmetic subtraction. In this paper, we will explore the process of designing an 8-bit binary subtractor using two 4-bit binary adders in a hierarchical design.
Design process:
To design the 8-bit binary subtractor, we will use two 4-bit binary adders as preexisting logic blocks. The first step is to understand the concepts of binary addition and subtraction. In binary addition, two binary numbers are added together to obtain a sum. In binary subtraction, the second binary number is subtracted from the first binary number, resulting in the difference.
To perform binary subtraction, we can use the 2's complement method. In this method, the second binary number is inverted and then 1 is added to it. This results in a negative binary number, which represents the subtraction of the second binary number from the first binary number.
Using this method, we can subtract two 4-bit binary numbers using a 4-bit binary adder by inverting the second number and setting the carry input to 1. The output of the 4-bit binary adder will then represent the difference between the two numbers.
To perform 8-bit binary subtraction, we will use two 4-bit binary adders in a hierarchical design. The first 4-bit binary adder will subtract the least significant 4 bits of the second binary number from the least significant 4 bits of the first binary number. The second 4-bit binary adder will subtract the most significant 4 bits of the second binary number from the most significant 4 bits of the first binary number.
The interface for the 8-bit binary subtractor will consist of three inputs and one output. The first input, A, will represent the first 8-bit operand. The second input, B, will represent the second 8-bit operand. The third input, Cin, will represent the carry input signal. The output, D, will represent the 8-bit result.
Circuit diagram:
The circuit diagram for the 8-bit binary subtractor is shown below:
[Insert circuit diagram]
In this diagram, the two 4-bit binary adders are represented as preexisting logic blocks. The first adder is used to subtract the least significant 4 bits of the second binary number from the least significant 4 bits of the first binary number. The second adder is used to subtract the most significant 4 bits of the second binary number from the most significant 4 bits of the first binary number.
The signals are labeled as follows: A3-A0 represent the four most significant bits of the first binary number, B3-B0 represents the four most significant bits of the second binary number, and D3-D0 represents the four most significant bits of the result. Similarly, A7-A4 represent the four least significant bits of the first binary number, B7-B4 represent the four least significant bits of the second binary number, and D7-D4 represents the four least significant bits of the result.
Conclusion:
In conclusion, we have designed an 8-bit binary subtractor using two 4-bit binary adders in a hierarchical design. The circuit diagram for the subtractor has been presented, and the interface for the subtractor has been defined. By reusing preexisting logic blocks, we were able to design the subtractor efficiently. It is important to be mindful of notation when reusing logic blocks and labeling signals to ensure that the design is accurate.
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