odd parity os Original number = 1010

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written 2.2 years ago by

Original number = 1010

Odd parity

For 4-bit, 3 parity bits $p_1, p_2, p_3$ are appended in locations 1,2,4 respectively.

Position	1	2	3	4	5	6	7
-	P1	P2	D1	P3	D2	D3	D4
original number	-	-	1	-	0	1	0
odd parity in positions 1.3.5.7 requires P1 = 0	0	-	1	-	0	1	0
odd parity in positions 2,3,6,7 requires P2 = 1	0	1	1	-	0	1	0
odd parity in positions 4,5,6,7 requires P3 = 0	0	1	1	0	0	1	0

$\therefore$ Hamming code for 1010 with odd parity os 0110010

$(-89)_{10}$

Binary :

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$\therefore$ $(89)_{10}$

$= (01011001)_2$

1. signed magnitude

since, the number is negative, sign bit = 1

magnitude = 01011001

$\therefore$ $(-89)_{10} = (101011001)_2$

2. 1's complement,

$(-89)_{10} = (10100110)_2$

1's complement of $(-89)_{10}$ = 10100110

3. 2's complement,

2's complement = 1's complement + 1

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$\therefore$ 2's complement of $(-89)_{10} = 10100111$

$(BC5)_H - (A2B)_H$

15's complement of A2B,

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$\therefore$ 16's complement of A2B = 5D4 + 1 = 5D5

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since, carry is generated answer is positive, and discard carry to get final answer.

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