Advantages of the automated binary number system over decimal system


Ever since the CD appeared as the first digital music medium for consumers in the early 80's, digitization of the audio world has progressed steadily. Commercial sound systems are being designed to take advantage of the numerous merits of digital technology as well. Here's a brief summary of the basics of digital audio.

In digital audio systems, analog audio signals are converted to digital numeric data that is then transmitted and processed while in digital form. Values represented as a series of ones and zeroes are known as "binary" values, as opposed to the "decimal" values made up of the ten numbers from "0" to "9" that we use on a daily basis. Since sound is basically vibrations travelling through air, as we saw in the "What is Sound? That's why digital technology is currently concentrated in the mixing and processing stages of the sound system.

This leads to the question: Noise is lurking in every stage of any sound system, from the microphone at the input to the speakers at the output. And wherever there are long cable runs there's a chance that more noise will infiltrate the system causing distortion of the signal. This is the same for both analog and digital systems. There were counter wheels and relay components. Aiken was greatly concerned with the apperance of the machine, and dispite war time and lack of materials, Mark I was covered with steel and glass.

Mark I was a very flexible machine, although it was not that automatical as its original name suggests, while much of its operation had to be set manually. Mark I was, in modern terms, a parallel synchronous calculator with a word length of 24; 23 decimal digits and one sign. Calculations are performed decimally with fixed decimal point. The operation unit of the machine consisted of 72 registers called accumulators.

Each accumulator held 24 electromagnetical rotary switches, individually connected by a clutch to a drive shaft, by which decimal units, carry, and timing information were stored.

This provides for a digit number plus a sign. The accumulators are complete addition and subtraction machines and functions as a storage or memory device. There is no clear separation between storage and arithmetic functions. Some of the accumulators are dedicated to a special function, such as accumulator 70 that deals with the absolute value of a quantity, accumulator 70 that can increase the data amount to be stored on expense on accurancy , or accumulator 72 that is the automatic check counter.

Accumulators Addition with carry, example: There are 72 places where addition could be performed , but only one for multiplication. That depends on the fact how IBM's card reader was constructed, but appearently also because of Aiken simply liked addition. Separate devices took care of multiplication and division. The actual multiplcation involves multiple addition; by withdrawal such many multiples of the multiplicand as it's indicated by the multiplier, and then adding them together.

Division on the other hand, are multiple subtractions. There were 60 constant registers that consisted of position rotary switches on which digit signed numbers could be set or retrived through computation. These registers would correspond to what we call programmable ROM, but Mark I's ROM could not in comparison to modern computers, store programs, but simple supplied with numberical constants. Each register contained 24 dial switches which corresponds to 24 digits.

They are decimal in that they use the familiar ten numbers '0' to '9' and they are digital in the sense that only whole numbers are recognized as valid. Number values are represented by gear wheels and each digit of a number has its own wheel. If a wheel comes to rest in a position intermediate between whole number values, the value is regarded as indeterminate and the engine is designed to jam to indicate that the integrity of the calculation has been compromised.

Jamming is a form of error-detection. Babbage considered using number systems other than decimal including binary as well as number bases 3, 4, 5, 12, 16 and He settled for decimal out of engineering efficiency - to reduce the number of moving parts - as well as for their everyday familiarity. Babbage began in with Difference Engine No. The design describes a machine to calculate a series of values and print results automatically in a table.

Integral to the concept of the design is a printing apparatus mechanically coupled to the calculating section and integral to it. From time to time Babbage changed the capacity of the Engine. The design shows a machine calculating with sixteen digits and six orders of difference. The Engine called for some 25, parts shared equally between the calculating section and the printer.

Had it been built it would have weighed an estimated four tons and stood about eight feet high. Work was halted on the construction of the Engine in following a dispute with the engineer, Joseph Clement.

Government funding was finally axed in With the construction project stalled, and freed from the nuts and bolts of detailed construction, Babbage conceived, in , a more ambitious machine, later called Analytical Engine, a general-purpose programmable computing engine.