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.

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

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.