When the result of a subtraction is negative, the 1000v10 is added back into the binary register and no increment is made to the BCD registers. The second, third and fourth calls on the subroutine cause the subtraction of 100v10, 10v10 and 1 respectively from the binary numbers and the addition of 100v16, 10v16 and 1 into the BCD register. Each subroutine call is complete when the result of a subtraction is a negative number.

ADDITIONAL PROBLEMS

1. Develop RTM systems to perform BCD complementation, add 1, x10, /10, multiplication, division, single and double precision.

2. Perform an analysis which compares the cost/speed of the arithmetic flowcharts which operate on BCD numbers without conversion and those routines which perform the equivalent operations with conversion from BCD to binary on input and binary to BCD on output.

3. Design a DMgpa which would facilitate BCD arithmetic. Carry out problem 1 above, based on this design.

TIME-BASED SYSTEMS: CLOCKS, TIMERS

WAVEFORM GENERATOR, AND WAVEFORM ANALYZER

INTRODUCTION

This section presents systems which synthesize (generate) and analyze time dependent functions. Carrying information in a time-dependent function is called modulation, converting information into such a function is called synthesis (encoding), and extracting information from such a function is called analysis (decoding). The primitive clock, delay, and integrating delay, classified as controls in Chapter 2, form the basis for time measurement, permitting encoding and decoding functions of time. The types of systems to be considered are shown in Figure Time-i. The first three (and variations) are, fundamentally, components for use in larger systems, whereas the last two might stand alone as independent systems.

The first two systems, K(clock) and K(delay), with and without variable time parameters, were presented as primitive RTM components in Chapter 2 and as. design problems in Chapter 3.

The third system, a K(clock and calendar), maintains a clock and calendar 'relative to a base point. The time is made available as output data either on a continuous basis or on demand. Such a design problem is presented in a following section and such a clock is interfaced to a digital computer in Chapter 6.

The fourth type of system, the waveform synthesizer (generator), is usually a combination of a clock (or timer) and a Data operation part which computes an output value at times t, t + st,.. . The output value, which is a function of any input parameters specified and the time, is either an analog (continuous) or a digital (discrete) waveform. The square wave generator presented in Chapter 3 is a simple example of a discrete waveform generator. Additional, more complex waveform generators will be presented in a following section.

The remaining system of interest, the D(waveform analyzer), is an analytic device which takes information from an input waveform, 1(t), and decodes it in an attempt to reduce the amount of information needed to represent the waveform; the reduced set of data is the output of the analyzer. For example, analyzers might measure the instantaneous amplitude of a waveform, waveform duration, or the number of occurrences per unit time that a signal has remained in a given

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