# Solution ## a) Design and Shifting Operation ### Given: - **Building block:** 4x4 barrel left-shifter - **Required:** 20x4 barrel left-shifter using the 4x4 shifter - **Input (X):** E5B27 (hexadecimal) - **Shift:** Left by 3 positions (bits) - **Output:** In hexadecimal --- ### Step 1: Convert Input to Binary E5B27 (hexadecimal) → binary: - E = 111 - 5 = 0101 - B = 1011 - 2 = 001 - 7 = 0111 So, E5B27 = 111 0101 1011 001 0111 --- ### Step 2: Shift Left by 3 Bits Shifting left by 3 bits, fill in zeros at the right: | Original bits: | 1 1 1 1 1 1 1 1 1 1 1 1 | |:--------------:|:--------------------------------------------:| | Shifted bits: | 1 1 1 1 1 1 1 1 1 1 1 | But since the input is 20 bits and shifting left by 3 bits, the new 20-bit number is: - [Original bits] << 3 = 17 leftmost bits from original, plus 3 zeros at right So, 111 0101 1011 001 0111 shift left 3: 0101 1011 001 0111 000 But let's explicitly write it out: Original: `111 0101 1011 001 0111` Shift left by 3 (drop the top 3 bits, append 000): - Remove leftmost 3 bits: `111` - Remaining: ` 0101 1011 001 0111` - Append 3 zeros: ` 0101 1011 001 0111 000` So, in groups of 4 bits: `001 1101 1001 0011 100` --- ### Step 3: Convert Back to Hexadecimal | Binary | Hex | |-----------------|-----| | 001 | 2 | | 1101 | D | | 1001 | 9 | | 0011 | 3 | | 100 | 8 | **Result:** **2D938** --- ## b) Logic Circuit of the Tristate Buffer You are asked to draw the logic circuit of a tristate buffer. ### Tristate Buffer Logic Symbol - **Input:** A - **Enable:** EN (active HIGH) - **Output:** Y | EN | A | Y | |----|---|---| | | X | Z (high impedance) | | 1 | | | | 1 | 1 | 1 | **Logic Circuit Diagram:** ``` A ─────┬───────────────┐ │ │ │ [AND]─────┬─── Y │ │ │ [EN]──┬───────────┘ │ │ │ └────[NOT]──[AND]────┘ ``` But the conventional tristate buffer is often shown as: - Input A goes to output Y if EN is HIGH; otherwise, output is high impedance. ``` _______ A ─────▶| |──────▶ Y | BUF | EN ────▶|_______| (enable) ``` --- ## **Summary Table** | **Step** | **Result** | |---------------------------|------------------| | Shift E5B27 left by 3 | **2D938** (hex) | --- ### **To Summarize** - **Shifted output:** `2D938` - **Tristate buffer logic:** See the above logic symbol/diagram. --- Let me know if you need a block diagram for the (20x4) barrel shifter using (4x4) shifters!

# Detailed Explanation of the Solution ## a) Design and Shifting Operation ### Step 1: Convert Input to Binary **Input:** Hexadecimal value: `E5B27` To convert each hexadecimal digit to binary: - **E** = 1110 - **5** = 0101 - **B** = 1011 - **2** = 0010 - **7** = 0111 Thus, the complete binary representation of `E5B27` is: ``` E5B27 = 1110 0101 1011 0010 0111 ``` ### Step 2: Shift Left by 3 Bits **Task:** Shift the binary number left by 3 positions. When shifting left: 1. Move all bits to the left by 3 places. 2. Fill the rightmost 3 positions with zeros. **Original bits:** ``` 1110 0101 1011 0010 0111 ``` After shifting left by 3 positions, the bits look like this: ``` 1110 0101 1011 0010 0111 → 111001011011001000000 ``` However, since we are limited to a 20-bit result, we need to truncate excess bits. The 20-bit result is: ``` 0001 1100 1011 0010 0000 ``` ### Step 3: Convert Back to Hexadecimal Now, we convert the resulting 20-bit binary back to hexadecimal. We split the binary into groups of 4 bits: ``` 0001 → 1 1100 → C 1011 → B 0010 → 2 0000 → 0 ``` Thus, the hexadecimal representation of the shifted binary is: ``` 1CB20 ``` ### Final Output The shifted output in hexadecimal after left-shifting `E5B27` by 3 bits is **1CB20**. --- ## b) Logic Circuit of the Tristate Buffer ### Tristate Buffer Functionality A tristate buffer has three states: 1. **Output High (1)** - When enabled (EN = 1) and input (A) is 1. 2. **Output Low (0)** - When enabled (EN = 1) and input (A) is 0. 3. **High Impedance (Z)** - When disabled (EN = 0), the output is in a high impedance state, effectively disconnecting the output from the circuit. ### Logic Circuit Diagram The logic circuit consists of: - **Input (A)** to the buffer. - **Enable (EN)** signal controlling the output. - **Output (Y)** reflecting the state of input A when enabled. The basic logic structure is represented as: ``` _______ A ─────▶| |──────▶ Y | BUF | EN ────▶|_______| (enable) ``` ### Explanation of the Diagram - When **EN = 1**: - The input A is passed directly to output Y. - When **EN = 0**: - The output Y enters a high impedance state (not driven). --- ## Summary Table | **Step** | **Result** | |---------------------------|------------------| | Shift E5B27 left by 3 | **1CB20** (hex) | --- ### Conclusion - The shifted output for the input `E5B27` after a left shift of 3 is **1CB20**. - The tristate buffer allows control over the output state based on the enable signal. If you have further questions or need additional explanations, feel free to ask!