Binary numbers

Binary numbers are base – 2 numbers and have only two values – 0 and 1. The binary number system is based on two-level logic, conventionally noted as 0 or low level and 1 or high level. It is a system with a radix of two. It is considered in Digital Electronics.

EXAMPLE 1: Convert the decimal number 13  into binary numbers.
The decomposition of the number 13 in powers of 2 is written as:
13₁₀ = (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰)
= 1101₂

EXAMPLE 2: Convert the decimal number 125 into binary numbers.

For the number 125, we have:
125₁₀ = (1 × 2⁶) + (1 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 1111101₂

The binary code that is then obtained for a positive number is called a natural binary code. The coefficients or numbers (0 or 1) used in the binary representation of a number are called bits. The right-most bit is called the least significant bit (LSB), while the left-most bit
is called the most significant bit (MSB).

In practice, the conversion of a decimal number to a binary number can be carried out by reading, from last to first, the remainders of a series of integer divisions as illustrated by the above Figure. The arithmetic and logic unit of a microprocessor manipulates binary numbers or words with a fixed number of bits.

Binary Number Chart

The numbers from 1 to 10 can be expressed in a binary number system in the following way #

Operations on Binary Numbers 

Binary Addition

To find the answer to the addition, we add the binary integers digit by digit. The table below should be kept in mind while you add the two binary numbers. #

Binary Subtraction

The answer is found by subtracting the digit of the binary number by a digit. Two binary numbers are subtracted while keeping in mind the table below. #

Binary Number Example

• Convert the binary number 0001. #
  The decimal equation for the conversion is 0 + 0 + 0 + 1 = 1 decimal
• Convert the binary number 0110.
  The decimal equation for the conversion is 0 + 4 + 2 + 0 = 6 decimal
• Convert the binary number 1110.
  The decimal equation for the conversion is 8 + 4 + 2 + 0 = 14 decimal
• Convert the binary number 1111.
  The decimal equation for the conversion is 8 + 4 + 2 + 1 = 15 decimal

Tips to Remember Binary Number

• Binary addition is also referred to as the “AND” operation. #
• Binary multiplication is also called an “OR” operation.
• A binary number consists of two numbers 0 and 1.
• Binary numbers are represented with 2 at their base. For example, $(101{)}_{2.}$
• Each digit in a binary number is referred to as a bit. For example, $(111{)}_2$ is a three-bit binary system.