# Tag: Octal and Hexadecimal 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…