# Machine Architecture and Number Systems. Major Computer Components. Schematic Diagram of a Computer. The CPU. The Bus. Main Memory.

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1 1 Topics Machine Architecture and Number Systems Major Computer Components Bits, Bytes, and Words The Decimal Number System The Binary Number System Converting from Decimal to Binary Major Computer Components Central Processing Unit (CPU) Bus Main Memory (RAM) Secondary Storage Media I / O Devices 2 Schematic Diagram of a Computer The CPU Central Processing Unit The brain of the computer Controls all other computer functions In PCs (personal computers) also called the microprocessor or simply processor. Diagram taken from Java Concepts, Fourth Edition 3 4 The Bus Computer components are connected by a bus. A bus is a group of parallel wires that carry control signals and data between components. Main Memory Main memory holds information such as computer programs, numeric data, or documents created by a word processor. Main memory is made up of capacitors. If a capacitor is charged, then its state is said to be 1, or ON. We could also say the bit is set. If a capacitor does not have a charge, then its state is said to be 0, or OFF. We could also say that the bit is reset or cleared. 5 6

3 13 Number Systems The on and off states of the capacitors in RAM can be thought of as the values 1 and 0, respectively. Therefore, thinking about how information is stored in RAM requires knowledge of the binary (base 2) number system. Let s review the decimal (base 10) number system first. The Decimal Number System The decimal number system is a positional number system. Example: X 10 0 = X 10 1 = 20 6 X 10 2 = X 10 3 = The Decimal Number System The decimal number system is also known as base 10. The values of the positions are calculated by taking 10 to some power. Why is the base 10 for decimal numbers? Because we use 10 digits, the digits 0 through 9. The Binary Number System The binary number system is also known as base 2. The values of the positions are calculated by taking 2 to some power. Why is the base 2 for binary numbers? Because we use 2 digits, the digits 0 and The Binary Number System The binary number system is also a positional numbering system. Instead of using ten digits, 0-9, the binary system uses only two digits, 0 and 1. Example of a binary number and the values of the positions: X 2 0 = X 2 1 = 0 1 X 2 2 = = = 16 1 X 2 3 = = = 32 0 X 2 4 = = = 64 0 X 2 5 = = 8 1 X 2 6 =

4 19 Converting from Decimal to Binary Practice conversions: Binary Decimal Make a list of the binary place values up to the number being converted. Perform successive divisions by 2, placing the remainder of 0 or 1 in each of the positions from right to left. Continue until the quotient is zero. Example: Practice conversions: Working with Large Numbers =? Decimal Binary Humans can t work well with binary numbers; there are too many digits to deal with. Memory addresses and other data can be quite large. Therefore, we sometimes use the hexadecimal number system The hexadecimal number system is also known as base 16. The values of the positions are calculated by taking 16 to some power. Why is the base 16 for hexadecimal numbers? Because we use 16 symbols, the digits 0 through 9 and the letters A through F. Binary Decimal Hexadecimal Binary Decimal Hexadecimal A B C D E F

5 25 Example of a hexadecimal number and the values of the positions: 3 C 8 B Example of Equivalent Numbers Binary: Decimal: Hexadecimal: 50A7 16 Notice how the number of digits gets smaller as the base increases. 26 Converting from Binary to Hex Converting from Binary to Octal Because 16 is the equivalent of 2 4, it is easy to convert from binary to hex and vice-versa. Binary: Hex: 0x D 2 F 0 Octal is another number system that is base 8. Because 8 is the equivalent of 2 3, it is easy to convert from binary to octal and vice-versa. Convert the following binary number to octal:

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