## How to implement multiplication by 5 for BCD code?

Interviewees who are not familiar with BCD code, we recommend to read this link first.

Assume the BCD code value is within the range between 0 and 9. Thus we can use the table below to show the inputs and outputs of the multiplier.

## Design a circuit that detects if one input is a delayed version of the other

Assuming 1b input A is generated by a random sequence, 1b input B is a delayed version of A. The delay value varies, and can be [1, 10] (inclusive).

Design a circuit, that takes A and B as inputs, and Y as output. If B is guaranteed to have 1s, then Y should be 1.

## How to implement pseudo LRU?

We discussed true LRU implementations, but they are usually costly. In this post, we will explain how to implement pseudo LRU.

An example is shown below. The data structure is similar to a binary tree. For N ways in a cache set, we need to keep (N – 1) bits. If there are 8 sets in a way, then we will need 7 bits.

Upon a cache access, all tree nodes point to that cache way will be flipped. For example, if set 3 is accessed, then h0, h1 and h4 will be flipped in next cycle.

To find LRU, we can perform a depth-first-search starting from h0, and traverse nodes in lower levels. If the node is 0, then we traverse the left sub-tree; otherwise, we traverse the right sub-tree. In the diagram above, the LRU is set 3.

Once we understand the basic idea of pseudo LRU, it is easy to write code for pseudo LRU.

## How to implement true LRU? (II)

We covered 2 true LRU implementations: square matrix implementation and counter based implementation in previous post. We will discuss 2 more true LRU implementations in this post.

In the following discussion, we assume the number of ways in a cache set is N.

## Linked List Implementation

Linked list is probably the most straightforward LRU implementation. Nodes are linked from head to tail. Head points to the most recently used item, while tail points to the least recently used item.

Upon a cache access, the corresponding node “jumps” to the head, and the previous head becomes the next node of new head.

## How to implement true LRU? (I)

Least Recently Used, or LRU, is the optimal cache replacement policy, and it is used in various applications where arbitration is required. In this post, we will discuss different true LRU implementations, based on the paper “Highly Efficient LRU Implementations for High Associativity Cache Memory”.

In the following discussion, we assume the number of ways in a cache set is N.

## Design A Programmable Sequence Detector

If the sequence is not predefined, then we can no longer use traditional FSM based sequence detector. Assuming we know the sequence to detect is 5-bit, then we can use the following circuit to detect the sequence.

The circuit consists of a 5-stage shift register, and a 5-bit configuration register. The sequence to detect is programmed in the configuration register, and the input sequence is compared with the configuration register every cycle.

## Determine Whether An Infinite Sequence Is A Multiple of 5

Assuming incoming bit stream is one bit per cycle, design a circuit that detects whether the integer number formed by the bit stream is a multiple of 5.

The idea is to have an FSM consisting of 5 states, S0, S1, S2, S3, S4. Each state represents divided by 5 remainder in previous cycle. If FSM stays at S0, then it means the number could be divided by 5 in previous cycle; otherwise, the number was not a multiple of 5.