COMPUTER NUMBER SYSTEMS & DIGITAL DEVICES By: Sohaib Rehman

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.  Example  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

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 * 2 2 ) + (0 * 2 1 ) + (1 * 2 0 ) =5 ( Decimal)  What is the decimal equivalent for ?

Binary Conversion  = ?  = ?  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 /161/256

Hexadecimal DecHexDecHex 0=08=8 1=19=9 2=210=A 3=311=B 4=412=C 5=513=D 6=614=E 7=715=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 Decimal529 BCD

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.  Example Binary Gray

Gray Code

Basic Digital Devices  Inverting & non-inverting buffers.  Logic Gates.  Programmable logic Devices ( PLD’s ).  PLA’s  PROM’s.

Basic Digital Devices  Latches  Flip Flops  Registers  Counters  ROM  RAM  Buses  ALU.

Reading Assignment  Binary, Decimal, Octal, Hexa Decimal number systems with their conversion and addition, subtraction, multiplication, division and digital devices.