EEC180 — DIGITAL SYSTEMS II — SPRING 2024 HOMEWORK 4

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EEC180 — DIGITAL SYSTEMS II — SPRING 2024

HOMEWORK 4

1) IEEE 754 Standard (50 points)

Consider the two numbers A = 3.0 and B = -3.5. We would like to use the IEEE 754 standard representation. In this problem, we assume an 8-bit representation with 1 bit for sign, 3 for exponent in excess-3 notation (means the bias is 3), and 4 bits for the mantissa.

1. What is the minimum positive number that can be represented if the significand is normalized? (8 points)

2. What is the maximum positive number that can be represented? (8 points)

3. What decimal number is represented by the bit pattern 10000001? (8 points)

4. Find the IEEE 754 binary representation of the numbers A and B. (10 points)

5. Compute P = A × B using the binary (not decimal) floating-point representations of A and B. (16 points)

2) Multiple-Port Memory (50 points).

Consider the 4-port SRAM shown below. The SRAM has three read/write ports and one read-only port. All read operations of this SRAM are combinational (asynchronous). The output signal busy2 is set to 1 when the write operation at port2 cannot proceed due to a concurrent write at the same address from port1. The output signal busy3 is set to 1 when the write operation at port3 cannot proceed due to a concurrent write at the same address from port1 or port2.

Write a complete Verilog model of the SRAM. Your model should be able to handle any special cases that may arise when using the SRAM.