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Introduction to the Binary System

Introduction to the Binary System

Get introduced to the base symbols and representation rules of the binary system.

What is the binary system?

The decimal system leverages the fact that humans have ten fingers to count with. The binary system does something similar in the case of computers.

An essential component of computers is the transistor, which has two states, on and off. These are sometimes also referred to as high and low states, and correspond to the presence or absence of voltage. Each state can be represented using one of two symbols—00 and 11—resulting in a numbering system with base 2.

The binary system is a two-base system.

Base digits

The base digits for the binary system are simple: 0 to represent a low state and 1 to represent a high state.

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Place value

Like in the decimal system, the rules for representing a number in binary come from the place values of the digits. We know that the rule was that place values correspond to ascending powers of 1010 from right to left.

Note: For the binary system, the rule is that—you guessed it—place values correspond to ascending powers of 22 from right to left.

Note: Recall that binary digits are referred to as bits.

MSB and LSB

MSB is the most significant bit. It is the leftmost bit of a binary number and the one with the largest place values. Similarly, the LSB, or least significant bit, is the rightmost bit and the one with a place value of 11. The same symbol 1 in different places can have different values. For example, in 001001, the MSB is 00, and in 100100 ...

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