# Tag: Binary Arithmetic

• ## 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 (two-valued) 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,…