Decimal to Binary 32 bit signed conversion

[Willjeezy]

Homework Statement

Convert -89 to 32 bit representation (2-complement for negative numbers)

my answer does not agree with calculated answers from multiple conversion sites.

Homework Equations

The Attempt at a Solution

to get the exponent i figured out the closest 2 exponent to 89, which is 7.

then I added the exponent to the bias, 127 + 7 = 134

therefore 134 to binary would be: (I added underscores to separate the sign/exponent and mantissa

1__________1 0 0 0 0 1 1 0___________0 1 1 0 0 1
sign___________exponent______________ mantissa

the only problem is when i check my answer on multiple sites, the answer is

1 __________1 0 0 0 0 1 0 1 ___________0 1 1 0 0 1

_____________________^---exponent they have adds up to 133 ?

what am I doing wrong?

 

[Mark44]

Homework Statement

Convert -89 to 32 bit representation (2-complement for negative numbers)

my answer does not agree with calculated answers from multiple conversion sites.

Homework Equations

The Attempt at a Solution

to get the exponent i figured out the closest 2 exponent to 89, which is 7.

then I added the exponent to the bias, 127 + 7 = 134

therefore 134 to binary would be: (I added underscores to separate the sign/exponent and mantissa

1__________1 0 0 0 0 1 1 0___________0 1 1 0 0 1
sign___________exponent______________ mantissa

the only problem is when i check my answer on multiple sites, the answer is

1 __________1 0 0 0 0 1 0 1 ___________0 1 1 0 0 1

_____________________^---exponent they have adds up to 133 ?

what am I doing wrong?

Why are you converting to floating point form? The number you need to convert is an integer. You're making this much harder than it actually needs to be.

 

[vela]

what am I doing wrong?

As Mark44 noted, you're solving the wrong problem.

But to answer the question you asked anyway, you don't want 2⁷. You want 2⁶, the power of 2 that's closest to 89 but less than or equal to 89. This gives you
$$89 = 1.390625 \times 2^{64}$$ which has a mantissa with the integer part equal to 1, which is what you want if you're going to convert to floating-point format.

 

[SteamKing]

2^64? I think you blew my mind

89 = 1.390625 * 64

 

[SteamKing]

Hint: convert 89 to Hex.

 

[Mark44]

As Mark44 noted, you're solving the wrong problem.

But to answer the question you asked anyway, you don't want 2⁷. You want 2⁶, the power of 2 that's closest to 89 but less than or equal to 89. This gives you
$$89 = 1.390625 \times 2^{64}$$ which has a mantissa with the integer part equal to 1, which is what you want if you're going to convert to floating-point format.

vela was thinking 6 but mistakenly wrote 64.

2^64? I think you blew my mind

89 = 1.390625 * 64

 

[vela]

2^64? I think you blew my mind

89 = 1.390625 * 64

Oops. Thanks for catching that.