Mixing
Two's complement addition issue
0
$begingroup$
In a two's complement system, 16-bit binary numbers $0010010010010010$ and $1111110011111100$ can be represented in the decimal system as $9362$ and $-772$, correspondingly.
Now, from what I've read and seen in examples, in a two's complement system, subtracting $770$ from $9362$ will look like this:
$$begin{align}&0010010010010010
\+&1111110011111100
\=&1110000010001110end{align}$$
But this number is negative in a two's complement system and it does not represent $9362$. What am I doing wrong?
computer-science binary computational-mathematics floating-point
asked Jan 13 at 2:08
sequencesequence
4,24731336
$endgroup$
|
show 4 more comments
0
$begingroup$
In a two's complement system, 16-bit binary numbers $0010010010010010$ and $1111110011111100$ can be represented in the decimal system as $9362$ and $-772$, correspondingly.
Now, from what I've read and seen in examples, in a two's complement system, subtracting $770$ from $9362$ will look like this:
$$begin{align}&0010010010010010
\+&1111110011111100
\=&1110000010001110end{align}$$
But this number is negative in a two's complement system and it does not represent $9362$. What am I doing wrong?
computer-science binary computational-mathematics floating-point
asked Jan 13 at 2:08
sequencesequence
4,24731336
$endgroup$
3
$begingroup$
The addition is incorrect.
$endgroup$
– saulspatz
Jan 13 at 2:14
2
$begingroup$
There should be a carry into each of the two leftmost digit positions that make the two leftmost result digits 0. You also seem to have thrown away the carry into the eight bit position (from the left).
$endgroup$
– Henning Makholm
Jan 13 at 2:19
1
$begingroup$
Curiously, the carries are missing exactly in the two columns where there is an 1 in each addend and a carry coming in from the right. Are you sure your bitwise addition table has the right result for $1+1+1$? Try computing $3+3$ in binary (with four-bit words) and see if you get $6$ like you should.
$endgroup$
– Henning Makholm
Jan 13 at 2:22
1
$begingroup$
Independently of all this, 1111110011111100 cannot possibly be the representation of $-771$ because it clearly represents an even number: the least significant bit is 0. To negate a 2s-complement number you invert all the bits and then add 1. You've forgotten to add $1$.
$endgroup$
– Henning Makholm
Jan 13 at 2:26
1
$begingroup$
@sequence You still have "subtracting $771$" in your question. I believe you should change the number to $772$ for the statement to be correct. Also, subtracting $772$ from $9362$ results in $8590$, but you say your result "does not represent $9362$.
$endgroup$
– John Omielan
Jan 13 at 2:37
|
show 4 more comments
0
0
0
$begingroup$
In a two's complement system, 16-bit binary numbers $0010010010010010$ and $1111110011111100$ can be represented in the decimal system as $9362$ and $-772$, correspondingly.
Now, from what I've read and seen in examples, in a two's complement system, subtracting $770$ from $9362$ will look like this:
$$begin{align}&0010010010010010
\+&1111110011111100
\=&1110000010001110end{align}$$
But this number is negative in a two's complement system and it does not represent $9362$. What am I doing wrong?
computer-science binary computational-mathematics floating-point
asked Jan 13 at 2:08
sequencesequence
4,24731336
$endgroup$
In a two's complement system, 16-bit binary numbers $0010010010010010$ and $1111110011111100$ can be represented in the decimal system as $9362$ and $-772$, correspondingly.
Now, from what I've read and seen in examples, in a two's complement system, subtracting $770$ from $9362$ will look like this:
$$begin{align}&0010010010010010
\+&1111110011111100
\=&1110000010001110end{align}$$
But this number is negative in a two's complement system and it does not represent $9362$. What am I doing wrong?
computer-science binary computational-mathematics floating-point
computer-science binary computational-mathematics floating-point
asked Jan 13 at 2:08
sequencesequence
4,24731336
asked Jan 13 at 2:08
sequencesequence
4,24731336
edited Jan 15 at 18:30
sequence
asked Jan 13 at 2:08
sequencesequence
4,24731336
asked Jan 13 at 2:08
sequencesequence
4,24731336
asked Jan 13 at 2:08
sequencesequence
4,24731336
4,24731336
3
$begingroup$
The addition is incorrect.
$endgroup$
– saulspatz
Jan 13 at 2:14
2
$begingroup$
There should be a carry into each of the two leftmost digit positions that make the two leftmost result digits 0. You also seem to have thrown away the carry into the eight bit position (from the left).
$endgroup$
– Henning Makholm
Jan 13 at 2:19
1
$begingroup$
Curiously, the carries are missing exactly in the two columns where there is an 1 in each addend and a carry coming in from the right. Are you sure your bitwise addition table has the right result for $1+1+1$? Try computing $3+3$ in binary (with four-bit words) and see if you get $6$ like you should.
$endgroup$
– Henning Makholm
Jan 13 at 2:22
1
$begingroup$
Independently of all this, 1111110011111100 cannot possibly be the representation of $-771$ because it clearly represents an even number: the least significant bit is 0. To negate a 2s-complement number you invert all the bits and then add 1. You've forgotten to add $1$.
$endgroup$
– Henning Makholm
Jan 13 at 2:26
1
$begingroup$
@sequence You still have "subtracting $771$" in your question. I believe you should change the number to $772$ for the statement to be correct. Also, subtracting $772$ from $9362$ results in $8590$, but you say your result "does not represent $9362$.
$endgroup$
– John Omielan
Jan 13 at 2:37
|
show 4 more comments
3
$begingroup$
The addition is incorrect.
$endgroup$
– saulspatz
Jan 13 at 2:14
2
$begingroup$
There should be a carry into each of the two leftmost digit positions that make the two leftmost result digits 0. You also seem to have thrown away the carry into the eight bit position (from the left).
$endgroup$
– Henning Makholm
Jan 13 at 2:19
1
$begingroup$
Curiously, the carries are missing exactly in the two columns where there is an 1 in each addend and a carry coming in from the right. Are you sure your bitwise addition table has the right result for $1+1+1$? Try computing $3+3$ in binary (with four-bit words) and see if you get $6$ like you should.
$endgroup$
– Henning Makholm
Jan 13 at 2:22
1
$begingroup$
Independently of all this, 1111110011111100 cannot possibly be the representation of $-771$ because it clearly represents an even number: the least significant bit is 0. To negate a 2s-complement number you invert all the bits and then add 1. You've forgotten to add $1$.
$endgroup$
– Henning Makholm
Jan 13 at 2:26
1
$begingroup$
@sequence You still have "subtracting $771$" in your question. I believe you should change the number to $772$ for the statement to be correct. Also, subtracting $772$ from $9362$ results in $8590$, but you say your result "does not represent $9362$.
$endgroup$
– John Omielan
Jan 13 at 2:37
3
3
$begingroup$
The addition is incorrect.
$endgroup$
– saulspatz
Jan 13 at 2:14
$begingroup$
The addition is incorrect.
$endgroup$
– saulspatz
Jan 13 at 2:14
2
2
$begingroup$
There should be a carry into each of the two leftmost digit positions that make the two leftmost result digits 0. You also seem to have thrown away the carry into the eight bit position (from the left).
$endgroup$
– Henning Makholm
Jan 13 at 2:19
$begingroup$
There should be a carry into each of the two leftmost digit positions that make the two leftmost result digits 0. You also seem to have thrown away the carry into the eight bit position (from the left).
$endgroup$
– Henning Makholm
Jan 13 at 2:19
1
1
$begingroup$
Curiously, the carries are missing exactly in the two columns where there is an 1 in each addend and a carry coming in from the right. Are you sure your bitwise addition table has the right result for $1+1+1$? Try computing $3+3$ in binary (with four-bit words) and see if you get $6$ like you should.
$endgroup$
– Henning Makholm
Jan 13 at 2:22
$begingroup$
Curiously, the carries are missing exactly in the two columns where there is an 1 in each addend and a carry coming in from the right. Are you sure your bitwise addition table has the right result for $1+1+1$? Try computing $3+3$ in binary (with four-bit words) and see if you get $6$ like you should.
$endgroup$
– Henning Makholm
Jan 13 at 2:22
1
1
$begingroup$
Independently of all this, 1111110011111100 cannot possibly be the representation of $-771$ because it clearly represents an even number: the least significant bit is 0. To negate a 2s-complement number you invert all the bits and then add 1. You've forgotten to add $1$.
$endgroup$
– Henning Makholm
Jan 13 at 2:26
$begingroup$
Independently of all this, 1111110011111100 cannot possibly be the representation of $-771$ because it clearly represents an even number: the least significant bit is 0. To negate a 2s-complement number you invert all the bits and then add 1. You've forgotten to add $1$.
$endgroup$
– Henning Makholm
Jan 13 at 2:26
1
1
$begingroup$
@sequence You still have "subtracting $771$" in your question. I believe you should change the number to $772$ for the statement to be correct. Also, subtracting $772$ from $9362$ results in $8590$, but you say your result "does not represent $9362$.
$endgroup$
– John Omielan
Jan 13 at 2:37
$begingroup$
@sequence You still have "subtracting $771$" in your question. I believe you should change the number to $772$ for the statement to be correct. Also, subtracting $772$ from $9362$ results in $8590$, but you say your result "does not represent $9362$.
$endgroup$
– John Omielan
Jan 13 at 2:37
|
show 4 more comments
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3071629%2ftwos-complement-addition-issue%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
draft saved
draft discarded
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3071629%2ftwos-complement-addition-issue%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
3
$begingroup$
The addition is incorrect.
$endgroup$
– saulspatz
Jan 13 at 2:14
2
$begingroup$
There should be a carry into each of the two leftmost digit positions that make the two leftmost result digits 0. You also seem to have thrown away the carry into the eight bit position (from the left).
$endgroup$
– Henning Makholm
Jan 13 at 2:19
1
$begingroup$
Curiously, the carries are missing exactly in the two columns where there is an 1 in each addend and a carry coming in from the right. Are you sure your bitwise addition table has the right result for $1+1+1$? Try computing $3+3$ in binary (with four-bit words) and see if you get $6$ like you should.
$endgroup$
– Henning Makholm
Jan 13 at 2:22
1
$begingroup$
Independently of all this, 1111110011111100 cannot possibly be the representation of $-771$ because it clearly represents an even number: the least significant bit is 0. To negate a 2s-complement number you invert all the bits and then add 1. You've forgotten to add $1$.
$endgroup$
– Henning Makholm
Jan 13 at 2:26
1
$begingroup$
@sequence You still have "subtracting $771$" in your question. I believe you should change the number to $772$ for the statement to be correct. Also, subtracting $772$ from $9362$ results in $8590$, but you say your result "does not represent $9362$.
$endgroup$
– John Omielan
Jan 13 at 2:37