# number conversions

2.7k views
represent number 6248 in

BCD

excess three code

2421 code

6311 code

edited

BCD : 0110 0010 0100 1000

EX-3 : 1001 0101 0111 1011

2421 : 1100 0010 0100 1110

6311 :1000 0011 0110 1011

selected
0
What should be the representation of 6 in 2421 ?

1100  or  0110   or both are correct..
1
$1100$ AFAIK, generally we use $0$ at msb for $0-4$ and $1$ at msb for $5-9$

BCD conversation :- Convert each digit into groups of four binary digits equivalent.

6248 =   6 - 0110   2-0010  4 - 0100   8-1000

(6248)10 =  (0110 0010 0100 1000)
BCD

EXCESS THREE CODE :-

Add +3 in each digit then convert into groups of four binary digit equivalent.

### 6+3 = 9 , 2+3=5 , 4+3 = 7, 8+3 = 11,

(9)10 = (1001)excess3 , (5)10 = (0101)excess3, (7)10 = (0111)excess3,  (11)10 = (1011)excess3

Now,combine together (6248)10=(1001 0101 0111 1011)excess3

2421 CODE :-  Represent each decimal digit in binary with respect to weight 2 4 2 1.

6  = 0x21 + 1x22 + 1x21 + 0x20.             2  = 0x21+ 0x22 + 1x21 + 0x20.

4  = 0x21 + 1x22 + 0x21 + 0x20.             8 = 1x21 + 1x22 + 1x21 + 0x20.

combine all those. ANS :- (0110 0010 0100 1110)2421

6311 CODE :-  Represent each decimal digit in binary with respect to weight 6 3 1 1.

6  = 1x61 + 0x31 + 0x11 + 0x11.             2  = 0x61+ 0x31 + 1x11 + 1x11.

4  = 0x61 + 1x31+ 0x11 + 1x11.             8 = 1x61 + 0x31 + 1x11 + 1x11.

combine all those. ANS :- (1000 0011 0101 1011)6311

Thank you....
0

Why 6 is taken as 0110 & not 1100  in 2421 representation ?

1 vote
Assuming the number 6248 in decimal .

BCD :          0110  0010  0100 1000

Excess 3:    1001  0101  0111 1011

2-4-2-1        0110  0010  0100 1110    (This is not unique since the representation in 2-4-2-1 varies) Each digit is represented as the summation like 6 is obtained 4+2 , so bit position 4,2 is made 1 in the first digit )

6-3-1-1        1000  0011  0110  1011     (This representation is also not unique and is one of the representations.
0
yes 2-4-2-1 and 6-3-1-1 representations are not unique and varies and so complexities arises.

## Related questions

1
272 views
If N = 670 in base 9 system. Then find the radix complement of N.
A decimal number has $25$ digits. The number of bits required for its equivalent binary representation is approximately?? according to me I got $83$ but answer given Virtual gate is $75$please check??? I am right or wrong
Consider the (decimal) number $182$, whose binary representation is $10110110$. How many positive integers are there in the following set?$\{n\in \mathbb{N}: n\leq 182 \text{ and n has } \textit{exactly four} \text{ ones in its binary representation}\}$ $91$ $70$ $54$ $35$ $27$