Octal to binary and octal to hexa decimal conversions

DIGITAL LOGIC DESIGN ASSIGNMENT#1

Afrasiyab Haider BS-IT 4th 16-ARID-02

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1. How to perform addition in octal number system? Give 3 examples

The addition in octal number system can be performed by following the table below:

+ 0 1 2 3 4 5 6 7

0 0 1 2 3 4 5 6 7

1 1 2 3 4 5 6 7 10

2 2 3 4 5 6 7 10 11

3 3 4 5 6 7 10 11 12

4 4 5 6 7 10 11 12 13

5 5 6 7 10 11 12 13 14

6 6 7 10 11 12 13 14 15

7 7 10 11 12 13 14 15 16

Octal number system is based on only 8 numbers 0-7 so the other upcoming numbers will be written as follows:

8(8) (10(8)), 9(8) (11(8)), 10(8) (12(8)), 11(8) (13(8)), 12(8) (14(8)), 13(8) (15(8)), 14(8) (16(8))

Carry Ans

Examples:

436(8) 3720(8) 5630(8)

+ 512(8) + 6514(8) + 7450(8)

______ ______ _______

1150(8) 12434(8) 15300(8)

1 1 1 1



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2. How to perform subtraction in octal number system? Give 3 examples

The subtraction in octal number system is same as in other number systems. The only variation is the

quantity of borrow. In the decimal system, you had to borrow a group of 10(10). In the binary system, you borrowed a

group of 10(2). In the octal system you will borrow a group of 10(8).

Examples: Borrow

5730(8) 1023(8) 7776(8)

- 3520(8) - 424(8) - 7(8)

______ ________ _______

2210(8) 377(8) 7767(8)

3. Conversion from Decimal to Octal: Give 3 examples.

a) 1276(10)

8 1276

8 159 - 4

8 19 - 7

2 - 3

Ans= 2374(8)

1 1 1



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b) 4359(10)

8 4359

8 544 – 7

8 68 - 0

8 8 - 4

1 - 0

Ans= 10407(8)

c) 6985(10)

8 6985

8 873 - 1

8 109 - 1

8 13 - 5

1 - 5

Ans= 15511 (8)

4. Explain binary coded decimals and also give their counting table?

BCD or Binary Coded Decimal is that number system or code which has the binary

numbers or digits to represent a decimal number. A decimal number contains 10 digits (0-9). Now the

equivalent binary numbers can be found out of these 10 decimal numbers. In case of BCD the binary number

formed by four binary digits, will be the equivalent code for the given decimal digits. In BCD we can use the

binary number from 0000-1001 only, which are the decimal equivalent from 0-9 respectively. Suppose if a

number have single decimal digit then it’s equivalent Binary Coded Decimal will be the respective four binary

digits of that decimal number and if the number contains two decimal digits then it’s equivalent BCDwill be the

respective eight binary of the given decimal number. Four for the first decimal digit and next four for the second

decimal digit.

Hundreds tens units

0000 0000 0000



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Table given below shows the binary and BCD codes for the decimal numbers 0 to 15.

From the table below, we can conclude that after 9 the decimal equivalent binary number is of four bit but in

case of BCD it is an eight bit number. This is the main difference between Binary number and binary coded

decimal. For 0 to 9 decimal numbers both binary and BCD is equal but when decimal number is more than one

bit BCD differs from binary.

Decimal number Binary number Binary Coded Decimals

0 0000 0000

1 0001 0001

2 0010 0010

3 0011 0011

4 0100 0100

5 0101 0101

6 0110 0110

7 0111 0111

8 1000 1000

9 1001 1001

10 1010 0001 0000

11 1011 0001 0001

12 1100 0001 0010

13 1101 0001 0011

14 1110 0001 0100

15 1111 0001 0101



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5. Explain ASCII codes, Give their table?

ASCII was developed from telegraph code. Its first commercial use was as a seven-bit tele

printer code promoted by Bell data services. Work on the ASCII standard began on October 6, 1960, with the

first meeting of the American Standards Association's (ASA) (now the American National Standards Institute or

ANSI) X3.2 subcommittees.

Originally based on the English alphabet, ASCII encodes 128 specified characters into seven-bit integers.

Ninety-five of the encoded characters are printable: these include the digits 0 to 9, lowercase letters a to z,

uppercase letters A to Z, and punctuation symbols. In addition, the original ASCII specification included 33

non-printing control codes which originated with Teletype machines; most of these are now obsolete.

Decimal Alphabet

65 A

66 B

67 C

68 D

69 E

70 F

71 G

72 H

73 I

74 J

75 K

76 L

77 M

78 N

79 O

80 P

81 Q

82 R

Decimal Alphabet

83 S

84 T

85 U

86 V

87 W

88 X

89 Y

90 Z

91-96 Special characters

97 a

98 b

99 c

100 d

101 e

102 f

103 g

104 h

105 i

Decimal Alphabet

106 j

107 k

108 l

109 m

110 n

111 o

112 p

113 q

114 r

115 s

116 t

117 u

118 v

119 w

120 x

121 y

122 z

123-127 Special characters



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6. Explain Excess-3 code and Give its table.

Excess-3 or 3-excess binary code (often abbreviated as XS-3, 3XS or X3) or Stibitz code (after George

Stibitz, who built a relay-based adding machine in 1937) is a self-complementary binary-coded decimal (BCD)

code and numeral system. It is a biased representation. Excess-3 code was used on some older computers as

well as in cash registers and hand-held portable electronic calculators of the 1970s, among other uses.

Biased codes are a way to represent values with a balanced number of positive and negative numbers

using a pre-specified number N as a biasing value. Biased codes (and Gray codes) are non-weighted codes. In

excess-3 code, numbers are represented as decimal digits, and each digit is represented by four bits as the digit value plus 3 (the "excess" amount):

The smallest binary number represents the smallest value (0 − excess).

The greatest binary number represents the largest value (2N+1 − excess − 1).

Excess-3 / Stibitz code

Decimal Excess-

3 Stibitz BCD 8-4-2-1 Binary

3-of-6 CCITT extension

4-of-8 Hamming extension

−3 0000 pseudo-tetrade

N/A N/A N/A N/A


N/A N/A N/A N/A


N/A N/A N/A N/A

0 0011 0011 0000 0000 …10 …0011

1 0100 0100 0001 0001 …11 …1011

2 0101 0101 0010 0010 …10 …0101

https://en.wikipedia.org/wiki/BCD_8-4-2-1

https://en.wikipedia.org/wiki/Pseudo-tetrade

https://en.wikipedia.org/wiki/Pseudo-tetrade



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3 0110 0110 0011 0011 …10 …0110

4 0111 0111 0100 0100 …00 …1000

5 1000 1000 0101 0101 …11 …0111

6 1001 1001 0110 0110 …10 …1001

7 1010 1010 0111 0111 …10 …1010

8 1011 1011 1000 1000 …00 …0100

9 1100 1100 1001 1001 …10 …1100

10 1101 pseudo-tetrade

pseudo-tetrade

1010 N/A N/A


pseudo-tetrade

1011 N/A N/A


pseudo-tetrade

1100 N/A N/A

13 N/A N/A pseudo-tetrade

1101 N/A N/A


1110 N/A N/A


1111 N/A N/A



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7. Explain UNI code:

Unicode is a computing industry standard for the consistent encoding, representation, and

handling of text expressed in most of the world's writing systems. The latest version contains a repertoire of

136,755 characters covering 139 modern and historic scripts, as well as multiple symbol sets. The Unicode

Standard is maintained in conjunction with ISO/IEC 10646, and both are code-for-code identical.

The Unicode Standard consists of a set of code charts for visual reference, an encoding method and set of

standard character encodings, a set of reference data files, and a number of related items, such as character

properties, rules for normalization, decomposition, collation, rendering, and bidirectional display order (for

the correct display of text containing both right-to-left scripts, such as Arabic and Hebrew, and left-to-right

scripts). As of June 2017, the most recent version is Unicode 10.0. The standard is maintained by the Unicode

Consortium.

Unicode can be implemented by different character encodings. The Unicode standard defines UTF-

8, UTF-16, and UTF-32, and several other encodings are in use. The most commonly used encodings are UTF-

8, UTF-16 and UCS-2, a precursor of UTF-16.

UTF-8, dominantly used by websites (over 90%), uses one byte for the first 128 code points, and up to 4 bytes

for other characters. The first 128 Unicode code points are the ASCII characters; so an ASCII text is a UTF-8

text.



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8. Explain GRAY code

The reflected binary code (RBC), also known just as reflected binary (RB) or Gray

code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in

only one bit (binary digit). The reflected binary code was originally designed to prevent spurious output

from electromechanical switches. Today, Gray codes are widely used to facilitate error correction in digital communications such as digital terrestrial television and some cable TV systems.

Bell Labs researcher Frank Gray introduced the term reflected binary code in his 1947 patent

application, remarking that the code had "as yet no recognized name". He derived the name from the fact that it "may be built up from the conventional binary code by a sort of reflection process".

The code was later named after Gray by others who used it. Two different 1953 patent applications use "Gray

code" as an alternative name for the "reflected binary code"; one of those also lists "minimum error code" and

"cyclic permutation code" among the names. A 1954 patent application refers to "the Bell Telephone Gray

code".

Decimal Binary Gray 0 0000 0000 1 0001 0001

2 0010 0011 3 0011 0010

4 0100 0110 5 0101 0111

6 0110 0101 7 0111 0100

8 1000 1100 9 1001 1101

10 1010 1111

11 1011 1110 12 1100 1010

13 1101 1011 14 1110 1001

15 111 1000

Education

Octal to binary and octal to hexa decimal conversions