DIGITAL::CH2::Binary Arithmetic

BINARY ARITHMETIC Numbers versus numeration It is imperative to understand that the type of numeration system used to represent numbers has no impact upon the outcome of any arithmetical function (addition, subtraction, multiplication, division, roots, powers, or logarithms). A number is a number is a number; one plus one will

DIGITAL::CH1::Conversion from decimal numeration

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

DIGITAL::CH1::Octal and hexadecimal numeration

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

DIGITAL::CH1::Decimal versus binary numeration

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

DIGITAL::CH1::Systems of Numeration

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

DIGITAL::CH1::Numbers and symbols

This is a chapter from an ebook which was republished from — See Volume page for copyright notice. 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