polska03 wrote:

1) 10111 is a 5bit pattern that is express is excess-16 notation. What is the decimal number?

so i went 1x16^4 + 1x16^2 + 1x16^1=65809, but the answer is 7.

Excess-

`16`

notaton means that a numbers should be represented by the bit pattern equivalent to such number *plus*

`16`

. So, using `7`

as input, you have 16+7 = 23 = 10111b (2^4+2^2+2^1+2^0)

polska03 wrote:2) Convert 193(decimal) to a 10-but pattern using 2

s compliment notation/

Since

`193`

is positive, you haven't to complement (just use `193`

binary representation)193 = 0011000001b (2^7+2^6+2^0)

polska03 wrote:3)convert 3.4375(decimal) to an 8-bit floating point binarty patter that uses 1 bit for the sign, 3 bits for the exponent(excess-4 notation), and 4 bits of rthe manitssa.

I had no idea how to this one.

The sign is

`0`

since we have a positive number:sign = 0b

Usually there is an implicit leading

`1`

in the mantissa, as, for instance in "IEEE 754 standard". I will follow such a convention. Hence your `4`

bits mantissa is1.mmmm

i.e. a number ranging from

`1`

(1.0000b) to `1.9375`

(`1.1111b = 2^0+2^-1+2^-2+2^-3+2^-4`

); We need to multiply such a range by `2`

, to include the given number, (`2 < 3.4375 < 3.875`

), hence the exponent must be `1`

, that is `5`

in `4`

-excess notation:exponent = 101b

now the mantissa, we have:

3.375 = 11.011b < 3.4375 < 3.5 = 11.100b

We've to pick one (they are at same distance from the given number). I choose

`3.5=11.100b`

, hencemantissa = 1100b

The final result is the following eight bit number

01011100

(Hope it makes sense).

[

**added**]

polska03 wrote:for number 3, my prof gave told us the answer was 0 110 1110

That (probably) means your professor doesn't use the '

*implicit leading 1 in the mantissa*' convention; this way your mantissa is

.mmmm

and we need an exponent of

`2`

(need to multiply the mantissa by `4`

), that is `6`

in excess-`4`

notationexponent = 6 = 110b

so that

11.01b = 3.250 < 3.4375 < 3.500 = 11.10b

choosing

`11.10`

as best match, we obtain01101110

[/

**added**]

:)

--SA