By Jack Ganssle, Tammy Noergaard, Fred Eady, Lewin Edwards Lewin Edwards is an embedded engineer with over 15 years experience designing embedded systems hardware firmware and control software., David J. Katz, Rick Gentile, Ken Arnold, Kamal Hyder, Bob Per
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There’s no memory; past events have no impact on present outputs. An adder is a typical combinatorial device: the output is always just the sum of the inputs—no more, no less. The easiest way to understand how any combinatorial circuit works—be it a single component or a hundred interconnected ICs—is via a truth table, a matrix that deﬁnes every possible combination of inputs and outputs. 3). 3: The truth table for a wire’s output and input. In Out 0 0 1 1 Gates are the basic building blocks of combinatorial circuits.
One Hz means the waveform repeats once per second. A thousand Hz is a kHz (kilohertz), a million Hz is the famous MHz by which so many microprocessor clock rates are deﬁned, and a billion Hz is a GHz. The reciprocal of Hz is period. That is, where the frequency in hertz deﬁnes the signal’s repetition rate, the period is the time it takes for the signal to go through a cycle. Mathematically: Period in seconds ϭ 1 Ϭ frequency in Hz Thus, a processor running at 1 GHz has a clock period of 1 nanosecond—one billionth of a second.
It’s a grouping of three binary digits to represent the quantities 0 through 7. It’s less compact than hex but was well suited to some early mainframe computers that used 36-bit words. Twelve octal digits exactly ﬁlls one 36-bit word (12 times 3 bits per digit). Hex doesn’t quite divide into 36 bits evenly. Today, though, virtually all computers are 8, 16, 32, or 64 bits, all of which are cleanly divisible by 4, so the octal dinosaur is rarely used. To convert from one base to another, just remember that the following rule constructs any integer in any number system: Number ϭ … ϩ C4 ϫ b4 ϩ C3 ϫ b3 ϩ C2 ϫ b2 ϩ C1 ϫ b1 ϩ C0 Each of the C’s are coefﬁcients—the digit representing a value, and b is the base.