you dont need to know assembly or c to write your language, you can write it in any language you want, generally if it's a compiled language then the compiler is written to smartly translate the language into assembly, and then it is assembled and compiled again into a binary for a particular operating system...
Also most interpreters, for the sheer need of speed of execution, are written in C (more oftenly C++), but as Buffy could tell you, you can write a C compiler in Lisp, nothing's stopping you. Mind you most C compilers are written in C ( yes, go figure that one

) also most (well i only know of one, and a shell) C interpreters are written in C.
Point being, no, you dont need to know a low level language to make your own programming language. Infact a well-defined language would tend to attract programmers that will code it in a low-level language for you. There are a few books available on language design
David A. Watt - "Programming Language Design Concepts"
Raphael Finkel - "Advanced Programming Language Design"
Terrence W. Pratt and Marvin V. Zelkowitz - "Programming Languages: Design and Implementation"
Bruce J. MacLennan - "Principles of Programming Languages"
At least a couple of those above should be augmented with "Programming Language Pragmatics Second Edition" by Michael L. Scott
Also these three books in succession (they get progressively more hardcore, and they all talk about modern compiler techniques, loop optimization, SSA, all kinds of good stuff):
Kenneth C. Louden - "Compiler Construction: Principles and Practice" - (this is more of a course book for students)
Andrew W. Appel - "Modern Compiler Implementation in C" - (this is a book that those students read to ace the course and familiarize themselves with up-to-date practices)
Steven Muchnick - "Advanced Compiler Design and Implementation" - (this is the book for the students that can teach the course and have the professor learn things he's probably never heard before)
But also remember, if you go with my advise and get 5 books (one out of the first set, the pragmatics book and the last 3 on compiler design) its nearly a 500 dollar bill, books on advanced topics are not cheap... But my point is, programming language design is above the range of a tutorial, a good programming language takes knowledge and practice, psychology and imagination, a good knowledge of current languages, but not a drive to compete with any of them. Only then can you desing a language that stands out on its own...
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Microsoft, the leader in using innovative tactics to promote irksome experience, coupled with antiquated technology that's held together by a pyramid of makeshift afterthoughts.
Apple, the leader in using irksome tactics to promote innovative experience, coupled with an antiquated core that's enhanced by state-of-the-art afterthoughts.
Linux, the leader in not using any tactics to promote user-defined experience, coupled with state-of-the-art core enhanced by innovative afterthoughts.
