# Binary Number System

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Binary Number System

At the heart of every computer is a microprocessor, which is designed the actions of your PC. The processor, which is short for both microprocessor and central processor unit (CPU), is a piece of electronic circuitry that uses digital logic to perform the instructions of your software.

Like the light switch on the wall, the electricity in the computer is either on or off. Data is stored in the computer with electrical charges that are either on or off. In the early days of the computer, vacuum tubes, which were about the size and shape of small light bulbs, stored data by turning individual tubes on or off. In today’s computers, this same concept is applied on a much smaller scale with the transistor. Like the vacuum tube, the transistor holds an electrical charge that is—yes, you guessed it—on or off.

The electrical charge in a transistor is one of two distinct electrical voltage levels. A higher voltage level represents one value, and a lower voltage level represents another value. Because the computer has only these two electrical states in which to store data, the data has to be either very simple, or some means must be used to allow multiple transistors to be grouped to represent more complex data.

The term binary loosely means “two numbers,” and the two numbers associated with binary are 1 and 0. Simply by assignment, the two voltage levels in the computer can represent these two binary values, with the lower voltage level equaling 0 and the higher voltage level equaling 1. The transistor can store either the voltage representing a 1 or a 0. When a transistor is assigned a binary value this way, it becomes a binary digit, or bit, for short. To store data larger than a single bit, groups of bits are combined. Here are some of the key digital elements involved with the digital logic of the computer:

The byte is used on the computer to store many types of data. The eight bits of the byte can hold the decimal values 0 to 255. The eight bits must be used to store from one to three digits, remember that only binary 1s and 0s can be stored in the byte’s bits. How these values are stored in a byte is by assigned each bit a different power of two value.

Understand that the first bit (bit 1) is the right-most bit in the byte. If you add all of the decimal values for each bit, the total is 255. The binary number 00000000 (the eight bits in a byte) represents 0 because none of the power of two values is used in the number. To put it another way, none of the power of two values was turned on. On the other hand, the binary value 11111111 represents 255 because all of the power to two values are turned on and therefore included in the number represented. If you wish to store a number larger than 255, you use more bits. This is where the machine word comes in. You can store the number 32,767 in 16 bits; 32 bits can hold the number 2,147,483,647; and 64 bits can represent the number 92,23,372,036,854,775,808.

Like the light switch on the wall, the electricity in the computer is either on or off. Data is stored in the computer with electrical charges that are either on or off. In the early days of the computer, vacuum tubes, which were about the size and shape of small light bulbs, stored data by turning individual tubes on or off. In today’s computers, this same concept is applied on a much smaller scale with the transistor. Like the vacuum tube, the transistor holds an electrical charge that is—yes, you guessed it—on or off.

The electrical charge in a transistor is one of two distinct electrical voltage levels. A higher voltage level represents one value, and a lower voltage level represents another value. Because the computer has only these two electrical states in which to store data, the data has to be either very simple, or some means must be used to allow multiple transistors to be grouped to represent more complex data.

The term binary loosely means “two numbers,” and the two numbers associated with binary are 1 and 0. Simply by assignment, the two voltage levels in the computer can represent these two binary values, with the lower voltage level equaling 0 and the higher voltage level equaling 1. The transistor can store either the voltage representing a 1 or a 0. When a transistor is assigned a binary value this way, it becomes a binary digit, or bit, for short. To store data larger than a single bit, groups of bits are combined. Here are some of the key digital elements involved with the digital logic of the computer:

- A bit (binary digit) is a single binary number that can be either 1 or 0.
- A binary word is one or more bits and usually ranges from 4 to 64 bits.
- A byte (pronounced “bite”; the common 8-bit binary word), is probably the computer storage unit you hear the most about. The memory and storage on the computer are normally expressed in bytes. A single byte can hold the binary values equal to 0 to 255 in decimal.
- A nybble (pronounced “nibble”), is a 4-bit binary word. It holds the binary equivalent of the decimal values 0 to 15. An 8-bit binary number is divided into two nybbles so it can hold two hexadecimal numbers.
- A machine word is the number of bits that are required to hold the largest binary number a microprocessor can process. The machine word is commonly used to refer to the bit size of the processor. For example, computers are often described as having a 16-bit processor, a 32-bit processor, or a 64-bit processor.

**Storing Data in a Byte**

The byte is used on the computer to store many types of data. The eight bits of the byte can hold the decimal values 0 to 255. The eight bits must be used to store from one to three digits, remember that only binary 1s and 0s can be stored in the byte’s bits. How these values are stored in a byte is by assigned each bit a different power of two value.

Understand that the first bit (bit 1) is the right-most bit in the byte. If you add all of the decimal values for each bit, the total is 255. The binary number 00000000 (the eight bits in a byte) represents 0 because none of the power of two values is used in the number. To put it another way, none of the power of two values was turned on. On the other hand, the binary value 11111111 represents 255 because all of the power to two values are turned on and therefore included in the number represented. If you wish to store a number larger than 255, you use more bits. This is where the machine word comes in. You can store the number 32,767 in 16 bits; 32 bits can hold the number 2,147,483,647; and 64 bits can represent the number 92,23,372,036,854,775,808.

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