Binary Numbers?

Question

1)What does it mean when a binary number is signed?

2)What does it mean when a binary number is signed magnitude?
eg: convert 11001101 to a signed magnitude number.

3)What does it mean when a binary number is unsigned?
eg: convert 175 to an unsigned binary number.

4) How would you work out a binary number that is to be divided. eg: 01100011 / 00001011

any help would be greatly appreciated.

I have searched online for an answer (at sites like wikipedia) but I still don't really understand the explanations that have been given.

Answer 1

1) either positive = 0 or negative = 1 the most significant bit ie furthest left
00000001 = one
00000000= zero
11111111= minus 1 ( to work out negative make all 0's to ones and add 1 to the result)
11111110= minus 2

range of numbers is -128 to 127 in an 8 bit form.

2) assume that 11001101 is unsigned. and make signed (in this case add a 0 on the LHS most significant bit.

3) just means convert to binary number.

4) I would convert to decimal work it out and then convert back.

Answer 2

There are 10 types of people in the world, those that understand binary and those that don't :)

Sorry couldn't resist!!

Been a while, but a signed binary number allows you to have negative numbers
an 8-bit number is normally 0-255, but a signed 8-bit number is from -128 to 127
ie; 00011011 = 27 if unsigned, whilst
00011011 = -27 if signed, the most significant figure determines wether the number is positive or negative

Hopefully that answers your questions about signed and unsigned numbers

Can't remember what the magnitude bit is, sorry

As for the division, i always found it easiest to convert to decimal, calculate and then convert back to binary

Answer 3

1) lets say we have 8 bits
unsigned: 0000 0000 to 1111 1111 (0 to 255)
signed: 1000 0000 to 0111 1111 (-128 to 127)

first bit from left (MSB) is interpreted as sign. if it is 1 the sign the number is negative

2)
3) see 1)

4) subtract repeatedly the second one from first one until the result is less then second one. the number of subtractions is quotient and the last result is the remainder

Some details:

to conver to decimal:
1 1 0 0 1 1 0 1 - binery number
7 6 5 4 3 2 1 0 - bit number (the power)

1*2^7+1*2^6+0*2^5+0*2^4 + 1*2^3+1*2^2+0*2^1+1*2^0 =
=128+64+0+0+8+4+0+1=205

to convert to binar:
175 = 1010 1111

175 / 2 = 87 and 1
87 / 2 = 43 and 1
43 / 2 = 21 and 1
21 / 2 = 10 and 1
10 / 2 = 5 and 0
5 / 2 = 2 and 1
2 / 2 = 1 and 0
1 / 2 = 0 and 1

Answer 4

In signed binary the first digit (most significant bit) represents whether the number is positive or negative. A 1 at the start indicates that the number is negative and a 0 positive. To divide a binary number you could first convert it into decimal then devide and convert the answer back again.

Answer 5

Try this set of links:
http://uk.search.yahoo.com/search?search=sums+with+binary&ei=UTF-8&fr=ks-ques&ico-yahoo-search-value=http%3A%2F%2Frds.yahoo.com%2F_ylt%3DAio9_W5NRNIsGwtHnMKyTQASBgx.%2FSIG%3D1140u5jk8%2F*-http%3A%2F%2Fuk.search.yahoo.com%2Fsearch&ico-wikipedia-search-value=http%3A%2F%2Frds.yahoo.com%2F_ylt%3DAvb_WchDBgUKJjqVGbJLqFwSBgx.%2FSIG%3D11ia1qo58%2F**http%253a%2F%2Fen.wikipedia.org%2Fwiki%2FSpecial%253aSearch&p=sums+with+binary