DE_MF

• Example: 835If n=4, then 104 -0835 = 10000If n=6, then 106-835= 1000000

0-835 =91650-000835=999165 12

1’s & 2’s Compleme The concept of negative sign is n Although there have been disp numbers in binary number syste been developed. The most popular of them a complement. Though 2's complement dominat but this is also used because hardware due to simpler concept

entsnot there in binary number system. putes about representing negativeem. And for it various methods haveall are 1's complement and 2's tes the 1's complement in popularitye of somewhat simpler design int. 13

1‘s complement The 1‘s complement of changing all 1s to 0s and al Example: the 1’s complimen

f a binary number is found byll 0s to 1s, asnt of 1001 is 0110 14

 2‘s complement = (1‘s comp Example: the 2’s complimen 1’s compliment o 2’s compliment o

plement) + 1nt of 1001 isof 1001 = 0110 +1of 1001 = 0111 15

2.3 Conversion of Numbe• The possibilities: Decimal Binary

er systems OctalHexadecimal 16

Quick Examp2510 = 110012 = 318 = 1 Base

ple1916 17

Decimal to Decimal (just Decimal Binary

t for fun) Octal Hexadecimal Next slide… 18

Decimal to Decimal (jus Decimal Binary

st for fun) Octal Hexadecimal Next slide… 19

Binary to DecimDecimal Binary

mal Octal Hexadecimal 20

Binary to Decimal• Technique – Multiply each bit by 2n, w the bit – The weight is the position on the right – Add the results

where n is the “weight” ofn of the bit, starting from 0 21

ExampleBit “0”1010112 => 1 x 20 = 1x2 0x2 1x2 0x2 1x2

e=1 2 21 = 0 22 = 8 23 = 0 24 = 32 25 = 4310

Hexadecimal to Octa 1F0C16 = ?8 1F 0001 1111 00 17 4

al0C000 1100 14 1F0C16 = 174148 23

Exercise – ConverDecimal Binary 33 1110101 Don’t use a ca

rt ... Octal Hexa- decimal 703 1AFalculator!

Exercise – Convert AnsweDecimal Binary 33 100001 117 1110101 451 111000011 431 110101111

…er Hexa- decimal Octal 41 21 165 75 703 1C3 657 1AF 25

2.4 BCD Code The 8421 code is called Decimal) code .BCD mea through 9 is represented by The designation 8421 indic four bits (23 , 22 ,21,20).The m is that conversion betwee decimal numbers is easy.

d the BCD (Binary Codedans that each decimal digit,y a binary code of four bit. ates the binary weights of the main advantage of BCD codeen 8421 code numbers and 26

2.4 BCD Code

27

Digital Codes - Gray Gray Code is a form of binary incrementing from one number to With Gray Code, only one bit c another. This feature allows a system checking (i.e. if more than one incorrect). The gray code is sometimes refe the first eight values compare wi reverse order.

yy that uses a different method ofo the next.changes state from one position to designer to perform some error e bit changes, the data must beerred to as reflected binary, because ith those of the last 8 values, but in 28

Digital Codes - GrayDecimal Bin 0 00 1 00 2 00 3 00 4 01 5 01

ynary Gray000 0000001 0001010 0011011 0010100 0110101 0111 29

Excess-3 code Excess-3 code is an examp 3 equivalent of a decimal n 3 and then converting it to a For instance to find excess number 4, first 3 is added equivalent of 7 i.e. 0111 form

ple of weighted code. Excess-number is obtained by addinga binary format.s-3 representation of decimal to 4 to get 7 and then binaryms the excess-3 equivalent. 30