Decimal to other codes conversions:
To convert decimal number into other system
with base ‘
r
’, divide integer part by r and multiply fractional part with
r
.
Other codes to Decimal Conversions:
Hexadecimal to Binary:
Convert each Hexadecimal digit into 4 bit binary.
2
16
1111)
(0101 1010
(5
)
5
AF
A
F
Binary to Hexadecimal:
Grouping of 4 bits into one hex digit.
Octal to Binary and Binary to Octal:
Same procedure as discussed above but here
group of 3 bits is made.
Codes:
Binary coded decimal (BCD):
In BCD code each decimal digit is represented with 4 bit binary format.
10
9
4
9
:(943)
1001 0100 0011
BCD
Eg
It is also known as 8421 code
Invalid BCD codes
Total Number possible
Valid BCD codes
10
Invalid BCD codes
These are 1010, 1011, 1100, 1101, 1110, and 1111
Excess-3 code: (BCD + 0011)
It can be derived from BCD by adding ‘3’ to each coded number.
It is unweighted and self-complementing code.
2
1
0
1
2
10
(
.
)
(A)
r
x x x
y y
2
1
2
2
1
0
1
2
A
x r
x r
x
y r
y
r
2
16
(110101.11)
0011 0101.1100
(35.C)
4
2
16
16
10
6

ECE FORMULA BOOK
3. DIGITAL ELECTRONICS AND CIRCUITS
[77]
Published by:
ENGINEERS INSTITUTE OF INDIA
.
ALL RIGHTS RESERVED
Gray Code:
It is also called minimum change code or unit distance code or reflected code.
Binary code to Gray code:
Gray code to Binary code:
Alpha Numeric codes:
EBCDIC (Extended BCD Interchange code)
It is 8 bit code. It can represent 128 possible characters.
Parity Method is most widely used schemes for error detection.
Hamming code is most useful error correcting code.
BCD code is used in calculators, counters.
Complements:
If base is
r
then we can have two complements.
(i) (r – 1)’
s
complement.
(ii) r’
s
complement.
To determine (r–1)’s complement
: First write maximum possible number in the
given system and subtract the given number.
To determine r’
s
complement:
(r–1)’
s
complement + 1
First write (r–1)’
s
complement and then add 1 to LSB
Example:
Find 7’
s
and 8’
s
complement of 2456
7777
5321
2456
1
7's complement
8's complement
5321
5322
Find 2’s complement of 101.110
1’s complement 010.001
For 2’s complement add 1 to the LSB
010.001
1
2'scomplement
010.010
+
1
0
0
1
0
+
+
+
1
1
0
1
1
MSB
MSB
Binary
Gray

ECE FORMULA BOOK
3. DIGITAL ELECTRONICS AND CIRCUITS
[78]
Published by:
ENGINEERS INSTITUTE OF INDIA
.
ALL RIGHTS RESERVED
Data Representation:
Unsigned Magritude:
Range with
n
bit
Signed Magritude:
Range with
n
bit
1’s complement:
Range with
n
bit
2’ complement:
With
n
bits Range
In any representation
+ve numbers are represented similar to +ve number in sign magnitude.
1
0 to 2
n
5
101
5
Not possible
1
1
(2
1) to
(2
1)
n
n
6
0110
sign bit
sign bit
with 4 bits
with 8 bits
6
1
110
1
0000110
1
1
(2
1) to
(2
1)
n
n
6
0110
sign bit
1's complement of 6
6
1
001
1
1
2
to (2
1)
n
n
6
0110
sign bit
2's complement of 6
6
1
010

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- Summer '16
- Jam Adam Scalin
- Binary numeral system, Binary-coded decimal, Voltage source, ECE FORMULA BOOK, Power dissipation