Radix 12 numbers; 9a.5, b.0a, ba.95, a55.a1, baa.baa Two\'s component format Enc

Question

Radix 12 numbers; 9a.5, b.0a, ba.95, a55.a1, baa.baa Two's component format Encode each of the following decimal numbers in 16-bit 2's complement format with 0,2,4 or 8 fractional bits; 6.4, 33.675, 123.45 references and Check the correctness of your conversions in parts by applying Horner's formula to the resulting 2 1/3 complement numbers to derive the decimal equivalents. Repeat part a for the following decimal numbers:-6.4, 33.675, -123.45 Repeat part b for the results of part c. Floating-point numbers

Explanation / Answer

Actually u needs to specify the number of bits given for the integer and the fractiional part.

For this example say we have 8 bit for each part then,

6.4 = 00000110.01100000

33.675 = 00100001.10100000

123.45 = 01111011.01100000

which is same as normal binary representation. see the fractional part is only approximation. as only 2,4,and 8 is used it is very crude.

b.

by horners rule we know that,

An An-1An-2.........A0  = -An*2n + An-1*2n-1 +An-2 *2n-2+.......+A0 + A-1 *2-1  + A-2 *2-2 +...........

here comparing this with the aboce expression we get that

6.4 = 0 * 27  + 0*26 +....1*22 + 1*21 +0*20 . + 0*2-1 +1*2-2 + 1*2-3 +........ = 6. 375---------------ans.

similarly for

33.675 = 0 * 27  + 0*26 +1*25 +.... +0*20 . + 1*2-1 +0*2-2 + 1*2-3 +........ = 33. 625---------------ans.

and

123.45 = 0 * 27  + 1*26 +1*25 + 1*24 +1*23+0*22 + 1*21 +1*20 . + 0*2-1 +1*2-2 + 1*2-3 +........ = 123. 375---------------ans.

c.

for the negative representation,

-6.4 = 11111001. 10100000

-33.675 = 11011110.01100000

-123.45 = 100000100.10000000

d. here again we can check the answer with the above given horner's rule. the most simple way to represent negative number by horner's rule is as following,

1. take the mod of that nuber.

2. substract that from the 2MSB where MSB is the most significant available for the number format.

3. represent that number using normal binary representation.

4. put 1 at the MSB.

that way also we cwn check that the above results are valid.---------------------------------ans.

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