Let's Program the Transistors
Digital Hardware Design
In the previous article, we have seen the representation of a binary number in IEEE 754 single-precision floating point format. In this article, we will do the reverse process, which means determining the value of a binary number from a floating-point representation. For this, we will use the following formula: Binary Number = (-1)S(1 +…
In the previous article, we got an overall idea about the representation of floating point number. In this article, we will specifically focus on the single-precision IEEE 754 representation of floating point numbers. Single precision format represents any floating point number in 32 bits. The following figure shows all the parts of the single precision…
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Imagine you have a processor with registers of size 32 bits. Can the processor store a number larger than 32 bits in one register? It is possible if the number is represented in floating point format. The floating point format is useful in representing very large and very small integer numbers without increasing the number…
Though the computers store everything in binary format, the user interface deals with the hexadecimal format for ease of understanding. For a human, it is easy to deal with hexadecimal than the stream of ones and zeros. So, in this article, we will study the arithmetic of hexadecimal numbers. One way to perform hexadecimal arithmetic…
We have learned from the article “addition of 2’s complement signed binary numbers” that overflow occurs if the carries into and out of MSB are different. In this article, we will solve some examples that highlight how to detect overflow and how to avoid overflow. Example: Perform the following binary addition in 2’s complement arithmetic….
If we have three binary bits, then we can represent eight numbers, starting from 0 to 7. So, in other words, 0 to 7 is the range of numbers that we can represent using three binary bits. However, this range is defined for unsigned magnitude numbers. In this article, we will get to know the…
In an earlier article, we learned about 2’s complement addition. In this article, we will discuss how to perform 1’s complement addition. We will consider the same example that is taken for the 2’s complement addition. Important Rule: Add the two numbers using the basic rules of binary addition. If there is a carry out…
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Many a time, overflow in a binary addition seems like a final carry generation. However, overflow leads to an incorrect sum, whereas carry does not. This is a little confusing if not understood correctly. So, let’s understand the overflow concept clearly. Imagine you have a half-tea-filled cup. Your friend has a jar with some amount…
Addition and subtraction of 2’s complement signed binary numbers are important learning concepts, as digital computers use 2’s complement representation. 2’s complement arithmetic follows all the basic rules of binary arithmetic. However, a few tricks need to be learned so that we can get the correct result in its 2’s complement form. This article discusses…
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Binary arithmetic is essential in all digital computers and in many other types of digital systems. Now, since we know about different number systems and signed numbers, this is the right time to learn about binary arithmetic and the associated rules. First, we would learn about the basic rules of binary arithmetic, and solve some…