Tag: Decimal versus Binary Numeration

1.6 Conversion From Decimal Numeration
Because octal and hexadecimal numeration systems have bases that are multiples of binary (base 2), conversion back and forth between either hexadecimal or octal and binary is very easy. Also, because we are so familiar with the decimal system, converting binary, octal, or hexadecimal to decimal form is relatively easy (simply add up the products…

1.5 Octal and Hexadecimal to Decimal Conversion
Although the prime intent of octal and hexadecimal numeration systems is for the “shorthand” representation of binary numbers in digital electronics, we sometimes have the need to convert from either of those systems to decimal form. Of course, we could simply convert the hexadecimal or octal format to binary, then convert from binary to decimal,…

1.4 Octal and Hexadecimal Numeration
Because binary numeration requires so many bits to represent relatively small numbers compared to the economy of the decimal system, analyzing the numerical states inside of digital electronic circuitry can be a tedious task. Computer programmers who design sequences of number codes instructing a computer what to do would have a very difficult task if…

1.3 Decimal versus Binary Numeration
Let’s count from zero to twenty using four different kinds of numeration systems: hash marks, Roman numerals, decimal, and binary: System: Hash Marks Roman Decimal Binary —— ——— —– —— —— Zero n/a n/a 0 0 One  I 1 1 Two  II 2 10 Three  III 3 11 Four  IV 4…

1.2 Systems of Numeration
The Romans devised a system that was a substantial improvement over hash marks, because it used a variety of symbols (or ciphers) to represent increasingly large quantities. The notation for 1 is the capital letter I. The notation for 5 is the capital letter V. Other ciphers possess increasing values: X = 10 L =…

1.1 Numbers and Symbols
The expression of numerical quantities is something we tend to take for granted. This is both a good and a bad thing in the study of electronics. It is good, in that we’re accustomed to the use and manipulation of numbers for the many calculations used in analyzing electronic circuits. On the other hand, the…