Introduction
If you are new to the world of computer science, you might have come across the term “signed binary number.” A signed binary number is a mathematical representation of a number in binary form, which includes a sign bit that indicates whether the number is positive or negative. In this article, we will discuss how to convert a signed binary number to decimal form.
Binary Number System
The binary number system is a base-2 number system that uses only two digits, 0 and 1. It is widely used in computer science and digital electronics. Each digit in a binary number is called a bit, and the position of the bit determines its value. The rightmost bit is the least significant bit (LSB), and the leftmost bit is the most significant bit (MSB).
Signed Binary Number
A signed binary number is a binary number that includes a sign bit. The sign bit is usually the leftmost bit, and it indicates whether the number is positive or negative. If the sign bit is 0, the number is positive, and if the sign bit is 1, the number is negative.
Two’s Complement
Two’s complement is a method for representing negative numbers in binary form. In this method, the sign bit is 1, and the rest of the bits represent the magnitude of the number in binary form. To convert a negative number in two’s complement form to decimal form, you need to take the two’s complement of the number and then convert it to decimal form.
Conversion Steps
The following steps can be used to convert a signed binary number to decimal form:
Step 1: Identify the Sign Bit
Identify the sign bit in the binary number. If the sign bit is 0, the number is positive, and if the sign bit is 1, the number is negative.
Step 2: Convert Magnitude to Decimal
Convert the magnitude of the number (all bits except the sign bit) to decimal form. Use the positional notation to determine the value of each bit, and then add up the values to get the decimal equivalent.
Step 3: Apply Sign
If the sign bit is 0, the number is positive, and the decimal equivalent is the same as the magnitude. If the sign bit is 1, the number is negative, and you need to subtract the magnitude from 2^n, where n is the number of bits in the binary number, to get the decimal equivalent.
Example
Let’s take the signed binary number 11010 as an example. The sign bit is 1, so the number is negative. The magnitude of the number is 1010, which is equivalent to 10 in decimal form.
To get the decimal equivalent of the signed binary number, we need to subtract the magnitude from 2^5 (since there are 5 bits in the binary number):
2^5 – 10 = 22
Therefore, the decimal equivalent of the signed binary number 11010 is -22.
Conclusion
Converting a signed binary number to decimal form is a simple process that requires you to identify the sign bit, convert the magnitude to decimal form, and apply the sign. By following the steps outlined in this article, you can easily convert any signed binary number to decimal form.
