Information given:
1) 2 X 8-bits input A and B
2) 1 X ?-bits function selector input
3) 1 X 8-bits output C
4) 1 bit overflow (designed as “flag O” )
Function selector are made up of:
1) A + B operation 7) A NOR B
2) A – Boperation 8) A XNOR B
3) A AND B 9) A RIGHT SHIFT (by) B
4) A OR B 10) A LEFT SHIFT (by) B
5) A XOR B 11) A CIRCULAR SHIFT L & R (by) B
6) A NAND B 12) Incremental of A + B
Explanation for function selector 12):
When input A + B , the output C will start from A A +1 A + 2 A +3 ... A+B
Show the incremental value from A to A + B using programming and the timing delay is 1sec
Summary of operation:
Display Input A Display Input B Display Output C LED
Timer
1 2 3 ON
4 5 6 OFF
7 8 9 RESET
0 A B ENTER
X X X
X X X
X X X
X X X
Keypad
1) The input A and B will have a 3-decimal display to represent the decimal values of the keyed-in 8-bits input
2) When input A is selected (by pressing A in the keypad) , pressing the value of input A will be displayed at the display input A after pressing “ENTER”.
3) Step 2 is the same for input B
4) After displaying input A and B, choose a function in the function selector to display output C at the display output C.
5) when an overflow is detected, the LED at display output C will be switched on.
6) for the function number 12th, Timer must display the timing delay of 1sec
Problems:
1) How many bits of function selector should be used? Explain why.
2) Design a full logic circuit diagram of this entire operation. Must show all the logic gates involved
Tips: ( must have Multiplexer , demultiplexer , decoder, encoder ,shift register, 7-segment display , memory(RAM or ROM) ,ALU , timer and other suitable logic circuit)
3) what is the typical operating voltage for this circuit? Frequency?
Extra question:
1) as the maximum value of decimal for 8-bits is 255, what would happen if a higher value of decimal is keyed-in? for example, if we key in 355 in the input A, what would be displayed in the output C? Describe the response of the circuit regarding to the input.
2) Say we want to key in a number “123” to input A , but we accidentally press 124 instead. By using “RESET” in the keypad, describe the operation of the circuit when the number “4” is reset to 3. Tips:(involve Shift register and Memory)
3) When a 3-bits input A is added to 3-bits input B, the addition may cause an overflow of 1 bit,causing the LED to be switched on.We wish to know the value of the overflow bit.Describe how do we display the overflow bit (0,1,2…9)?
Tips: use a set of LED to show the number of the overflow.when a LED is ON,the value is 1.when a led is OFF,the value is 0.use 4 LED
Decimal value
0 0 0 0 0
0 0 0 1 1
0 0 1 0 2
1 0 0 1 9
Can you elaborate a bit on that?
1) How many bits of function selector should be used? Explain why.
To select between 12 different functions, we need to use at least 4 bits for the function selector. This is because with 4 bits, we can represent up to 2^4 = 16 different values. Since we only have 12 different functions, 4 bits are sufficient. Using more than 4 bits would be wasteful and would not provide any additional functionality.
2) Design a full logic circuit diagram of this entire operation. Must show all the logic gates involved.
Unfortunately, without a clear diagram or further specifications, I cannot provide a complete logic circuit diagram for this operation. However, I can provide an overview of the components typically involved in such a circuit:
- Multiplexer: Used for selecting different inputs based on the function selector input.
- Demultiplexer: Used for routing the inputs to the correct outputs based on the function selector input.
- Decoder: Used for decoding the function selector input into select lines for the multiplexer and demultiplexer.
- Encoder: Used for encoding the output of the logic circuit into a binary value for display.
- Shift Register: Used for shifting the bits for left and right shift operations.
- 7-Segment Display: Used for displaying the decimal values.
- Memory (RAM or ROM): Used for storing intermediate values during computations.
- ALU (Arithmetic Logic Unit): Used for performing arithmetic and logic operations.
- Timer: Used for timing delays.
- Other suitable logic gates: such as AND, OR, XOR, etc., used for implementing the specific logic functions.
Please note that the actual circuit design and implementation may vary based on specific requirements, technologies used, and constraints.
3) What is the typical operating voltage for this circuit? Frequency?
The typical operating voltage for such a circuit would depend on the specific components and technologies used. However, common operating voltage levels for digital circuits are 3.3V, 5V, or 12V. The frequency of operation would also vary based on the specific requirements, but common frequencies for digital circuits range from a few megahertz (MHz) to several gigahertz (GHz).
Extra Questions:
1) As the maximum value of decimal for 8-bits is 255, what would happen if a higher value of decimal is keyed-in? For example, if we key in 355 in the input A, what would be displayed in the output C? Describe the response of the circuit regarding the input.
If a higher value of decimal, such as 355, is keyed-in for the 8-bit input A, the circuit would not be able to correctly represent and process this value. Since the maximum value that can be represented by 8 bits is 255 (1111 1111 in binary), any value greater than this would cause an overflow. In this case, the output C would not display the correct result, and the overflow flag (O) would be set.
2) Say we want to key in a number "123" to input A, but we accidentally press 124 instead. By using "RESET" in the keypad, describe the operation of the circuit when the number "4" is reset to 3. Tips: (involve Shift register and Memory)
To reset the number "4" to "3" in input A using the "RESET" function, the circuit would need to store the previous value of input A (124) and then update it to the desired value (123) when the "RESET" button is pressed.
One possible approach would involve using a shift register and memory:
1. When the number 124 is entered into input A and "ENTER" is pressed, the value of input A is stored in a memory location.
2. The shift register is then used to shift the bits of the binary representation of input A to the left or right, depending on the function selected.
3. When the "RESET" button is pressed, the circuit retrieves the stored value from memory and updates input A with this value (123).
4. The shifted bits in the shift register are then adjusted accordingly to reflect the updated input A.
3) When a 3-bit input A is added to a 3-bit input B, the addition may cause an overflow of 1 bit, causing the LED to be switched on. We wish to know the value of the overflow bit. Describe how we display the overflow bit (0,1,2…9)? Tips: Use a set of LEDs to show the number of the overflow. When an LED is ON, the value is 1. When an LED is OFF, the value is 0. Use 4 LEDs.
To display the value of the overflow bit, we can use a set of 4 LEDs. Each LED will represent a bit, and when the value is 1, the corresponding LED will be turned on. When the value is 0, the corresponding LED will be turned off.
For example, if there is an overflow of 1 bit in a 3-bit addition, the fourth LED will be turned on, indicating the overflow. If there is no overflow, all 4 LEDs will be turned off.
To implement this, the circuit can compare the carry (overflow) bit from the addition operation and use appropriate logic gates (such as AND gates) to control the LEDs. When the carry bit is 1, the corresponding LED will be turned on. When the carry bit is 0, the corresponding LED will be turned off.