Converting Numbers to Sign/Magnitude and Two's Complement Notation in 8 Digits

[notorious9000]

Find (-5) to Sign / magnitude notation & Two's Complement in 8 digits

 

[xcvxcvvc]

Find (-5) to Sign / magnitude notation & Two's Complement in 8 digits

What have you tried so far? Do you know how to convert 5 into binary? That's your first step.

 

[notorious9000]

What have you tried so far? Do you know how to convert 5 into binary? That's your first step.

umm...
ex) for 4 digits
negative = 1000
positive = 0000

I guess 5 is a easy small number to make to binary

3210
-----
0101

is this right ?
so for Sign/Magnitude
1101 = -5

is this right ?

if this is right. how to convert this to Two's complement ?

 

[xcvxcvvc]

umm...
ex) for 4 digits
negative = 1000
positive = 0000

I guess 5 is a easy small number to make to binary

3210
-----
0101

is this right ?
so for Sign/Magnitude
1101 = -5

is this right ?

if this is right. how to convert this to Two's complement ?

Yeah. The way I learned to take two's complement is if you have a positive number, it is simply that number with a 0 in front to denote positivity. If the number is negative, you take the positive binary representation, invert all of its binary digits, and add one. Remember, if the number is positive, if you can pad the the 2's complement with as many 0s in front as you want. Oppositely, if the number is negative, you can pad the 2's complement with as many 1s in front as you want.

Example: represent 23 and -23 in 2's complement

2's complement of 23:
step 1: find the binary representation of 23
23 base 10 = 10111 base 2
step 2: add at least one 0 in front to denote positivity. However, infinitely many is ok
answer = 010111 or 000010111, etc.

2's complement of -23:
step 1 find the binary representation of 23:
23 base 10 = 10111 base 2
step 2: pad the number with 0s (you need enough. 1 usually does it). Note, after we take the one's complement (inverting each bit), these 0s will become 1s. Remember, you can pad a negative number with infinitely many 1s.
00010111
step 3: invert each bit:
11101000
step 4: add 1 to the least significant bit:
11101001

 

[DeeNos]

In sign/magnitude notation, (-5) would be represented as 10000101 in 8 digits. The first digit, 1, represents the sign (1 for negative) and the remaining 7 digits, 0000101, represent the magnitude (5 in binary form).

In two's complement notation, (-5) would be represented as 11111011 in 8 digits. This is achieved by first converting 5 to binary form (0101) and then taking the complement (1010) and adding 1, resulting in 1111. The first digit, 1, represents the sign (1 for negative) and the remaining 7 digits, 111011, represent the magnitude.

Both sign/magnitude and two's complement notations are commonly used in computer systems to represent negative numbers. Sign/magnitude notation is more intuitive as it directly shows the sign and magnitude of the number, while two's complement notation is more efficient for performing mathematical operations on negative numbers. It is important for scientists to be familiar with both notations in order to accurately represent and manipulate data in computer systems.