Computer Arithmetic
Now that binary numbers are discussed, it’s time to look at how their arithmetic works. But
there are two basic binary number representations so far. Unsigned binary numbers and binary
numbers that are represented using the sign and magnitude method.
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Now that binary numbers are discussed, it’s time to look at how their arithmetic works. But
there are two basic binary number representations so far. Unsigned binary numbers and binary
numbers that are represented using the sign and magnitude method.
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Addition & subtraction for signed binary integers (using sign and magnitude)
💎If the binary numbers are signed then addition and subtraction can be expressed using just the
addition operation.
💎Take a look at the following equations.
📌X – Y = X + (- Y )
📌-X – Y = (- X ) + (- Y)
📎Recap: The first bit of the binary number indicates sign, 0 for positive and 1 for negative
🔑Rules:
1. Identify the sign of each binary number [ the sign bit is excluded for the calculation]
A. If they both have the same sign
📌Add the two binaries.
📌Apply the sign to the result.
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💎If the binary numbers are signed then addition and subtraction can be expressed using just the
addition operation.
💎Take a look at the following equations.
📌X – Y = X + (- Y )
📌-X – Y = (- X ) + (- Y)
📎Recap: The first bit of the binary number indicates sign, 0 for positive and 1 for negative
🔑Rules:
1. Identify the sign of each binary number [ the sign bit is excluded for the calculation]
A. If they both have the same sign
📌Add the two binaries.
📌Apply the sign to the result.
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3) Multiplication for unsigned integers is straight
forward,
📌Find out the number of bits needed n
📌 Represent both numbers with n
📌 apply decimal multiplication rule
📌 apply the unsigned binary addition rule
📌cut-off unnecessary bits
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forward,
📌Find out the number of bits needed n
📌 Represent both numbers with n
📌 apply decimal multiplication rule
📌 apply the unsigned binary addition rule
📌cut-off unnecessary bits
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Division Rules:
📌Assumption
o n= number of bits of the divisor db1
o db2= dividend
📌cut n from db2 to create a smaller binary b
📌 if b is less than db1 then multiply db1 by 1
📌if b is greater than db1 then multiply db1 by 0
📌subtract and continue until the dividend is exhausted
💎apply the subtraction rule for unsigned integers
💎trim unnecessary bits
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📌Assumption
o n= number of bits of the divisor db1
o db2= dividend
📌cut n from db2 to create a smaller binary b
📌 if b is less than db1 then multiply db1 by 1
📌if b is greater than db1 then multiply db1 by 0
📌subtract and continue until the dividend is exhausted
💎apply the subtraction rule for unsigned integers
💎trim unnecessary bits
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Binary Complements
Complements are used to represent negative integers in a binary form.
💎Positive integers are
represented in the normal binary from.
✅ 1’s complement
Simply convert 0s to 1s and 1s to 0s.
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Complements are used to represent negative integers in a binary form.
💎Positive integers are
represented in the normal binary from.
✅ 1’s complement
Simply convert 0s to 1s and 1s to 0s.
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Subtraction using 1’s complement.
💎Since every negative integer can be represented uniquely subtraction can be replaced with addition. Like previously
X – Y = X + (-Y).
🔑Rule: If there is a remainder at the end it’s added to the result.
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💎Since every negative integer can be represented uniquely subtraction can be replaced with addition. Like previously
X – Y = X + (-Y).
🔑Rule: If there is a remainder at the end it’s added to the result.
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2’s compliment
💎This is a more refined version of 1’s compliment.
💎It solves the problem of 1’s complement.
💎To find the 2’s complement of a negative integer, first find the 1’s complement the add 1.
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💎This is a more refined version of 1’s compliment.
💎It solves the problem of 1’s complement.
💎To find the 2’s complement of a negative integer, first find the 1’s complement the add 1.
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Steps in SDLC
📌SDLC can be made up of multiple steps.
There is no concrete set number of steps involved.
📌Around seven or eight steps appear commonly;
however, there can be anywhere from five upwards to 12.
Typically, the more steps defined in an SDLC model,
the more granular the stages are.
💎In general, an SDLC methodology follows these following steps:
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📌SDLC can be made up of multiple steps.
There is no concrete set number of steps involved.
📌Around seven or eight steps appear commonly;
however, there can be anywhere from five upwards to 12.
Typically, the more steps defined in an SDLC model,
the more granular the stages are.
💎In general, an SDLC methodology follows these following steps:
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Steps in SDLC
📌SDLC can be made up of multiple steps.
There is no concrete set number of steps involved.
📌Around seven or eight steps appear commonly;
however, there can be anywhere from five upwards to 12.
Typically, the more steps defined in an SDLC model,
the more granular the stages are.
💎In general, an SDLC methodology follows these following steps:
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📌SDLC can be made up of multiple steps.
There is no concrete set number of steps involved.
📌Around seven or eight steps appear commonly;
however, there can be anywhere from five upwards to 12.
Typically, the more steps defined in an SDLC model,
the more granular the stages are.
💎In general, an SDLC methodology follows these following steps:
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1.Plan and requirements:
💎The new system requirements are defined. In particular, the deficiencies in the existing system must be addressed with specific proposals for improvement. Other factors defined include needed features, functions and capabilities.
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💎The new system requirements are defined. In particular, the deficiencies in the existing system must be addressed with specific proposals for improvement. Other factors defined include needed features, functions and capabilities.
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2. Analysis:
💎The existing system is evaluated. Deficiencies are identified. This can be done by interviewing users of the system and consulting with support personnel.
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💎The existing system is evaluated. Deficiencies are identified. This can be done by interviewing users of the system and consulting with support personnel.
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3. Design:
💎The proposed system is designed. Plans are laid out concerning the physical construction, hardware, operating systems, programming, communications and security issues.
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💎The proposed system is designed. Plans are laid out concerning the physical construction, hardware, operating systems, programming, communications and security issues.
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4. Implementation
The project takes shape during the implementation phase. This phase involves the construction of the actual project result. Programmers are occupied with encoding, designers are involved in developing graphic material, contractors are building, the actual reorganisation takes place. It is during this phase that the project becomes visible to outsiders, to whom it may appear that the project has just begun. The implementation phase is the doing phase, and it is important to maintain the momentum.
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The project takes shape during the implementation phase. This phase involves the construction of the actual project result. Programmers are occupied with encoding, designers are involved in developing graphic material, contractors are building, the actual reorganisation takes place. It is during this phase that the project becomes visible to outsiders, to whom it may appear that the project has just begun. The implementation phase is the doing phase, and it is important to maintain the momentum.
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💎Testing: All aspects of performance must be tested. If necessary, adjustments must be made at this stage. Tests performed by quality assurance (QA) teams may include systems integration and system testing.
💎Deployment: The system is incorporated in a production environment. This can be done in various ways. The new system can be phased in, according to application or location, and the old system gradually replaced. In some cases, it may be more cost-effective to shut down the old system and implement the new system all at once.
💎Upkeep and maintenance: This step involves changing and updating the system once it is in place. Hardware or software may need to be upgraded, replaced or changed in some way to better fit the needs of the end-users continuously. Users of the system should be kept up-to-date concerning the latest modifications and procedures.
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💎Deployment: The system is incorporated in a production environment. This can be done in various ways. The new system can be phased in, according to application or location, and the old system gradually replaced. In some cases, it may be more cost-effective to shut down the old system and implement the new system all at once.
💎Upkeep and maintenance: This step involves changing and updating the system once it is in place. Hardware or software may need to be upgraded, replaced or changed in some way to better fit the needs of the end-users continuously. Users of the system should be kept up-to-date concerning the latest modifications and procedures.
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