Tag: Overflow

2.6 Bit Grouping
The singular reason for learning and using the binary numeration system in electronics is to understand how to design, build, and troubleshoot circuits that represent and process numerical quantities in digital form. Since the bivalent (twovalued) system of binary bit numeration lends itself so easily to representation by “on” and “off” transistor states (saturation and…

2.5 Binary Overflow
One caveat with signed binary numbers is that of overflow, where the answer to an addition or subtraction problem exceeds the magnitude which can be represented with the alloted number of bits. Remember that the place of the sign bit is fixed from the beginning of the problem. With the last example problem, we used…

2.4 Binary Subtraction
We can subtract one binary number from another by using the standard techniques adapted for decimal numbers (subtraction of each bit pair, right to left, “borrowing” as needed from bits to the left). However, if we can leverage the already familiar (and easier) technique of binary addition to subtract, that would be better. As we…

2.3 Negative Binary Numbers
With addition being easily accomplished, we can perform the operation of subtraction with the same technique simply by making one of the numbers negative. For example, the subtraction problem of 7 – 5 is essentially the same as the addition problem 7 + (5). Since we already know how to represent positive numbers in binary,…

2.2 Binary Addition
The Rules of Binary Addition Adding binary numbers is a very simple task, and very similar to the longhand addition of decimal numbers. As with decimal numbers, you start by adding the bits (digits) one column, or place weight, at a time, from right to left. Unlike decimal addition, there is little to memorize in…

2.1 Numbers versus Numeration
It is imperative to understand that the type of numeration system used to represent numbers has no impact on 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 always equal two (so long as we’re dealing with real…