Number System & Digital Devices
To understand the structure of the binary number system, first step is to review the decimal or base-10 number system.
Example5 3 4 6 . 7 2103 102 101 100 10-1 10-2
This tells you that you have 5 thousands, 3 hundreds, 4 tens, 6 ones, 7 tenths and 2 hundredths.
Binary Number System
In a binary number system, each digit represents a power of 2.
A binary digit is often called a BIT. The binary system uses only two
numbers i.e. 1 & 0. Example of binary number system is
1 0 1 1 0 . 1 124 23 22 21 20 2-1
2-2
Binary Number System
To convert a binary number into its equivalent decimal number, multiply each digit times the decimal value of the digit and just add these up.
The binary number 101, represents(1 * 22) + (0 * 21) + (1 * 20)4 + 0 + 1 = 5 ( Decimal)
What is the decimal equivalent for 10110.11 ?
Binary Conversion
22710 = ?
10910 = ?
Conversion from decimal to binary is a simple method and is a part of a class exercise.
Hexadecimal
Computer require binary digits, so why use hexadecimal?
Example shows the digit values for hexadecimal which is often called hex.162 161 160 . 16-1 16-2
256 16 1 1/161/256
Hexadecimal
Dec Hex Dec Hex
0 = 0 8 = 81 = 1 9 = 92 = 2 10 = A3 = 3 11 = B4 = 4 12 = C5 = 5 13 = D6 = 6 14 = E7 = 7 15 = F
Binary-Coded Decimals
In applications such as frequency counters, digital voltmeters, or calculators, where the output is a decimal display, a BCD code is often used.
BCD uses a 4-bit binary code to represent each decimal digit in a number.
The simplest BCD code uses the first 10 numbers of standard binary code for the BCD numbers 0 through 9.
Binary-Coded Decimals
The Hexadecimals codes A through F are invalid BCD codes.
To convert a decimal number to its BCD equivalent, just represent each decimal digit by its 4-bit binary equivalent.
Example of BCD Decimal 5 2 9BCD 0101 00101001
Gray Code
Gray Code is another important binary code.
It is often used for encoding shaft position data from machines such as computer controlled latches.
Only one binary digit changes at a time as you count up in this code.
ExampleBinary 0000 0001 0010 0011
0100Gray0000 0001 0011 00100110
Basic Digital Devices
Inverting & non-inverting buffers.
Logic Gates.
Programmable logic Devices ( PLD’s ). PLA’s PROM’s.
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