Facebook
Google
GitHub
LinkedinDigital Circuits
Binary Math Circuits
11 questions By Tony R. Kuphaldt
-
Question 10 of 11
An arithmetic trick often used when working with the metric system is multiplication-by-ten and division-by-ten via shifting of the decimal point. A similar “trick” may be applied to binary numbers, with similar results.
Determine what sort of multiplication or division is accomplished when the “binary point” is shifted in a binary number. Research the datasheet of an arithmetic logic unit (ALU) circuit to see if and how this function is implemented.
Reveal answerShifting the “binary point” results in either multiplication or division by two. A multiplicative shift is performed by the 74AS181 ALU by arithmetic function selection 11002 (C16).
Challenge question: explain how multiplication or division by any binary quantity may be accomplished using successive bit-shifts and additions. For example, show what steps you could take to multiply any binary number by five (1012), using only “binary point” shifting and addition(s).
Notes:A lot of arithmetic tricks existing in the decimal numeration system are applicable, with slight revision, in the binary numeration system as well. This is a popular one, and often used by shrewd computer programmers to execute fast multiply-by-two or divide-by-two operations when “conventional” multiplication commands take more time.
-
Question 11 of 11
Explain the meaning of the digital lines A, B, F, and S in the following schematic diagram:
Reveal answerLines A, B, and F (with the slash marks and the number “4”) represent four actual conductors, carrying four bits of digital information. The thick line (S) is also a four-bit “bus” but is denoted by a slightly different convention.
In case you were wondering, it is unusual to mix two different bus symbol conventions in the same schematic diagram. I show this here only for your benefit, to see that there is more than one “standard” way to draw it.
Notes:The answer pretty much says it all. The fact that the IC is an ALU is quite incidental. Some students may research the part number to get a better understanding of what is going on. That is fine, but my emphasis in this question is the schematic diagram convention(s) for multi-conductor busses.
