# A Pipelined Multi-core MIPS Machine: Hardware Implementation by Mikhail Kovalev, Silvia M. Müller, Wolfgang J. Paul PDF

By Mikhail Kovalev, Silvia M. Müller, Wolfgang J. Paul

ISBN-10: 3319139053

ISBN-13: 9783319139050

ISBN-10: 3319139061

ISBN-13: 9783319139067

This monograph is predicated at the 3rd author's lectures on laptop structure, given in the summertime semester 2013 at Saarland college, Germany. It encompasses a gate point development of a multi-core computing device with pipelined MIPS processor cores and a sequentially constant shared memory.

The booklet includes the 1st correctness proofs for either the gate point implementation of a multi-core processor and likewise of a cache dependent sequentially constant shared reminiscence. This opens tips to the formal verification of synthesizable for multi-core processors within the future.

Constructions are in a gate point version and therefore deterministic. against this the reference versions opposed to which correctness is proven are nondeterministic. the improvement of the extra equipment for those proofs and the correctness evidence of the shared reminiscence on the gate point are the most technical contributions of this work.

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**Extra resources for A Pipelined Multi-core MIPS Machine: Hardware Implementation and Correctness Proof**

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Then e (a) = 1 would by hypothesis imply the contradiction e(a) = 1. Because in Boolean algebra e (a) ∈ B we conclude e (a) = 0. Thus, we have e(a) = e (a) for all a ∈ Bn . 1 Identities In this section we provide a list of useful identities of Boolean algebra. 6 Boolean Algebra 25 Table 4. Verifying the ﬁrst of de Morgan’s laws x1 0 0 1 1 • x1 ∧ x2 0 0 0 1 x2 0 1 0 1 x1 ∧ x2 1 1 1 0 x1 1 1 0 0 x2 1 0 1 0 x1 ∨ x2 1 1 1 0 De Morgan’s laws: x1 ∧ x2 ≡ x1 ∨ x2 x1 ∨ x2 ≡ x1 ∧ x2 Each of these identities can be proven in a simple brute force way: if the identity has n variables, then for each of the 2n possible substitutions of the variables the left and right hand sides of the identities are evaluated with the help of Table 3.

N-bit zero tester a a b b n n n n n n-eq 1 n-Zero 1 eq neq 1 eq (a) symbol 1 neq (b) implementation Fig. 13. n-bit equality tester The inputs a[n − 1 : 0], b[n − 1 : 0] and outputs eq, neq of an n-bit equality tester in Fig. 13 satisfy eq ≡ a = b , neq ≡ a = b . The implementation uses neq(a[n − 1 : 0]) = nzero(a[n − 1 : 0] ⊕ b[n − 1 : 0]) , eq = neq . An n-decoder is a circuit with inputs x[n − 1 : 0] and outputs y[2n − 1 : 0] satisfying ∀i : yi = 1 ↔ x = i . A recursive construction with k = one argues in the induction step n 2 is shown in Fig.

In Sect. , in [10,14]. Working out the proof sketch from [10], we formalize timing analysis and show by induction on depth that, with proper timing analysis, the detailed model is simulated by the digital model. This justiﬁes the use of the digital model as long as we use only gates and registers. In the very simple Sect. R of hardware conﬁgurations h. As we aim at the construction of memory systems, we extend in Sect. 5 both circuit models with open collector drivers, tristate drivers, buses, and a model of main memory.

### A Pipelined Multi-core MIPS Machine: Hardware Implementation and Correctness Proof by Mikhail Kovalev, Silvia M. Müller, Wolfgang J. Paul

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