Adder - Revision history

Rice: /* Ripple carry adder */

2024-05-13T15:35:18Z

Ripple carry adder

← Older revision		Revision as of 15:35, 13 May 2024
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	= Ripple carry adder =		= Ripple carry adder =
	A '''ripple carry adder''' is constructed with multiple full adders, linking each one's carry-out to the next's carry-in. It is capable of computing multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.		A '''ripple carry adder''' is constructed with multiple full adders, linking each one's carry-out to the next's carry-in. It is capable of computing multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.

			= Carry look-ahead adder =
			Some optimization can be done to make the ripple carry adder circuit more parallel for a faster propagation delay.

			A ''generate'' signal is ab. A ''propagate'' signal is a XOR b. Rewriting sum and carry in those terms can make the circuit more parallel

			<math>
			S_i=P_i \oplus C_{i-1}
			</math>

			<math>
			C_i=q_i+P_iC_{i-1}
			</math>

	== Overflow detection ==		== Overflow detection ==
	Consider two signed integers being operated on by our ripple carry adder. If there is an overflow, the last carry-in should be different from the first carry-out. Try proving it case by case. I gotta go do my machine learning lab now bye.		Consider two signed integers being operated on by our ripple carry adder. If there is an overflow, the last carry-in should be different from the first carry-out. Try proving it case by case. I gotta go do my machine learning lab now bye.
	[[Category:Computer Architecture]][[Category:ECS154A Midterm]]		[[Category:Computer Architecture]][[Category:ECS154A Midterm]]

Rice: /* Ripple carry adder */

2024-05-10T01:51:19Z

Ripple carry adder

← Older revision		Revision as of 01:51, 10 May 2024
Line 25:		Line 25:
	= Ripple carry adder =		= Ripple carry adder =
	A '''ripple carry adder''' is constructed with multiple full adders, linking each one's carry-out to the next's carry-in. It is capable of computing multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.		A '''ripple carry adder''' is constructed with multiple full adders, linking each one's carry-out to the next's carry-in. It is capable of computing multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.

			== Overflow detection ==
			Consider two signed integers being operated on by our ripple carry adder. If there is an overflow, the last carry-in should be different from the first carry-out. Try proving it case by case. I gotta go do my machine learning lab now bye.
	[[Category:Computer Architecture]][[Category:ECS154A Midterm]]		[[Category:Computer Architecture]][[Category:ECS154A Midterm]]

Rice at 20:19, 9 May 2024

2024-05-09T20:19:43Z

← Older revision		Revision as of 20:19, 9 May 2024
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	Full adders can be constructed with two half adders.		Full adders can be constructed with two half adders.

			== Circuit ==
			[[File:Full adder.png\|thumb\|Figure 1.]]
			Consider full adder that performs A + B = Y with carry-in and carry-out. After simplification with truth table and boolean algebra, we have

			<math>Y = (A\oplus B)\oplus C</math>

			<math>C_{in}=AB+(A\oplus B)C</math>

			with circuit shown in Figure 1.

	= Subtraction =		= Subtraction =
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	= Ripple carry adder =		= Ripple carry adder =
	A '''ripple carry adder''' is constructed with multiple full adders to ~~compute~~ multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.		A '''ripple carry adder''' is constructed with multiple full adders, linking each one's carry-out to the next's carry-in. It is capable of computing multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.
	[[Category:Computer Architecture]][[Category:ECS154A Midterm]]		[[Category:Computer Architecture]][[Category:ECS154A Midterm]]

Rice at 19:51, 9 May 2024

2024-05-09T19:51:47Z

← Older revision		Revision as of 19:51, 9 May 2024
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	Full adders can be constructed with two half adders.		Full adders can be constructed with two half adders.

			= Subtraction =
			The adder circuit can be used for subtraction without many changes. Simply negate the subtracted input, add a carry-in, and perform addition.

			The principle behind this is [[two's complement]].

	= Ripple carry adder =		= Ripple carry adder =
	A '''ripple carry adder''' is constructed with multiple full adders to compute multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.		A '''ripple carry adder''' is constructed with multiple full adders to compute multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.
	[[Category:Computer Architecture]][[Category:ECS154A Midterm]]		[[Category:Computer Architecture]][[Category:ECS154A Midterm]]

Rice at 19:49, 9 May 2024

2024-05-09T19:49:12Z

← Older revision		Revision as of 19:49, 9 May 2024
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	The '''~~ADD~~''' ~~operator~~ is the fundamental [[Instructions (Computer Science)\|instruction]] of many arithmetic operations (such as subtract, multiply, divide, and modulo).		The '''adder''' circuit is the fundamental [[Instructions (Computer Science)\|instruction]] of many arithmetic operations (such as subtract, multiply, divide, and modulo).

	= ~~Input~~ and ~~output~~ =		= Half and full adder =
	''ADD'' takes in two binary digits. It then outputs the result, which consists of a digit and a carry.		ADD takes in two binary digits. It then outputs the result, which consists of a digit and a carry.

	~~== Full adder ==~~
	In contrast to the above, which is a '''half adder''', a '''full adder''' has an additional input: '''carry-in''', which modifies the result.		In contrast to the above, which is a '''half adder''', a '''full adder''' has an additional input: '''carry-in''', which modifies the result.

	Full adders can be constructed with two half adders.		Full adders can be constructed with two half adders.

	== Ripple carry adder ==		= Ripple carry adder =
	A '''ripple carry adder''' is constructed with multiple full adders to compute multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.		A '''ripple carry adder''' is constructed with multiple full adders to compute multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.
	[[Category:Computer Architecture]][[Category:ECS154A Midterm]]		[[Category:Computer Architecture]][[Category:ECS154A Midterm]]

Rice: Rice moved page Add to Adder

2024-05-09T19:47:53Z

Rice moved page Add to Adder

← Older revision		Revision as of 19:47, 9 May 2024
(No difference)

Rice at 19:33, 9 May 2024

2024-05-09T19:33:30Z

← Older revision		Revision as of 19:33, 9 May 2024
Line 11:		Line 11:
	== Ripple carry adder ==		== Ripple carry adder ==
	A '''ripple carry adder''' is constructed with multiple full adders to compute multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.		A '''ripple carry adder''' is constructed with multiple full adders to compute multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.
	[[Category:Computer Architecture]]		[[Category:Computer Architecture]][[Category:ECS154A Midterm]]

Rice at 15:48, 22 April 2024

2024-04-22T15:48:57Z

← Older revision		Revision as of 15:48, 22 April 2024
Line 11:		Line 11:
	== Ripple carry adder ==		== Ripple carry adder ==
	A '''ripple carry adder''' is constructed with multiple full adders to compute multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.		A '''ripple carry adder''' is constructed with multiple full adders to compute multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.
			[[Category:Computer Architecture]]

Rice: /* Input and output */

2024-04-22T15:46:19Z

Input and output

← Older revision		Revision as of 15:46, 22 April 2024
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	''ADD'' takes in two binary digits. It then outputs the result, which consists of a digit and a carry.		''ADD'' takes in two binary digits. It then outputs the result, which consists of a digit and a carry.

			== Full adder ==
	In contrast to the above, which is a '''half adder''', a '''full adder''' has an additional input: '''carry-in''', which modifies the result.		In contrast to the above, which is a '''half adder''', a '''full adder''' has an additional input: '''carry-in''', which modifies the result.

			Full adders can be constructed with two half adders.

			== Ripple carry adder ==
			A '''ripple carry adder''' is constructed with multiple full adders to compute multi-digit addition. Each full adder contributes some propagation delay due to the need to input carry to the next full adder.

Rice: Created page with "The '''ADD''' operator is the fundamental instruction of many arithmetic operations (such as subtract, multiply, divide, and modulo). = Input and output = ''ADD'' takes in two binary digits. It then outputs the result, which consists of a digit and a carry. In contrast to the above, which is a '''half adder''', a '''full adder''' has an additional input: '''carry-in''', which modifies the result."

2024-04-22T15:13:38Z

Created page with "The '''ADD''' operator is the fundamental instruction of many arithmetic operations (such as subtract, multiply, divide, and modulo). = Input and output = ''ADD'' takes in two binary digits. It then outputs the result, which consists of a digit and a carry. In contrast to the above, which is a '''half adder''', a '''full adder''' has an additional input: '''carry-in''', which modifies the result."

New page

The '''ADD''' operator is the fundamental [[Instructions (Computer Science)|instruction]] of many arithmetic operations (such as subtract, multiply, divide, and modulo).

= Input and output =
''ADD'' takes in two binary digits. It then outputs the result, which consists of a digit and a carry.

In contrast to the above, which is a '''half adder''', a '''full adder''' has an additional input: '''carry-in''', which modifies the result.