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Q is a binary fixed point number format where the number of fractionalbits (and optionally the number of integer bits) is specified. For example, a Q15 number has 15 fractional bits; a Q1.14 number has 1 integer bit and 14 fractional bits. Q format is often used in hardware that does not have a floating-point unit and in applications that require constant resolution.
Characteristics[edit]
Q format numbers are notionally fixed point numbers, that is, they are stored and operated upon as regular binary signed integers, thus allowing standard integer hardware/ALU to perform rational number calculations. The number of integer bits, fractional bits and the underlying word size are to be chosen by the programmer on an application-specific basis – the programmer's choices of the foregoing will depend on the range and resolution needed for the numbers.
Some DSP architectures offer native support for common formats, such as Q1.15. In this case, the processor can support arithmetic in one step, offering saturation (for addition and subtraction) and renormalization (for multiplication) in a single instruction. Most standard CPUs do not. If the architecture does not directly support the particular fixed point format chosen, the programmer will need to handle saturation and renormalization explicitly with bounds checking and bit shifting.
There are two conflicting notations for fixed point. Both notations are written as Qm.n, where:
- Q designates that the number is in the Q format notation – the Texas Instruments representation for signed fixed-point numbers (the 'Q' being reminiscent of the standard symbol for the set of rational numbers).
- m. (optional, assumed to be zero or one) is the number of bits set aside to designate the two's complement integer portion of the number, exclusive or inclusive of the sign bit (therefore if m is not specified it is taken as zero or one).
- n is the number of bits used to designate the fractional portion of the number, i.e. the number of bits to the right of the binary point. (If n = 0, the Q numbers are integers – the degenerate case).
One convention includes the sign bit in the value of m,[1][2] and the other convention does not. The choice of convention can be determined by summing m+n. If the value is equal to the register size, then the sign bit is included in the value of m. If it is one less than the register size, the sign bit is not included in the value of m.
In addition, the letter U can be prefixed to the Q to indicate an unsigned value, such as UQ1.15, indicating values from 0.0 to +1.999969482421875 (that is, ).
Signed Q values are stored in two's complement format, just like signed integer values on most processors. In two's complement, the sign bit is extended to the register size.
For a given Qm.n format, using an m+n bit signed integer container with n fractional bits:
- its range is
- its resolution is
For a given UQm.n format, using an m+n bit unsigned integer container with n fractional bits:
- its range is
- its resolution is
For example, a Q15.1 format number: Ipack 2 3 4 x 5.
- requires 15+1 = 16 bits
- its range is [-214, 214 - 2−1] = [-16384.0, +16383.5] = [0x8000, 0x8001 … 0xFFFF, 0x0000, 0x0001 … 0x7FFE, 0x7FFF]
- its resolution is 2−1 = 0.5
Unlike floating point numbers, the resolution of Q numbers will remain constant over the entire range.
Conversion[edit]
Float to Q[edit]
To convert a number from floating point to Qm.n format:
- Multiply the floating point number by 2n
- Round to the nearest integer
Q to float[edit]
To convert a number from Qm.n format to floating point:
- Convert the number to floating point as if it were an integer, in other words remove the binary point
- Multiply by 2−n
Math operations[edit]
Q numbers are a ratio of two integers: the numerator is kept in storage, the denominator is equal to 2n.
Consider the following example:
- The Q8 denominator equals 28 = 256
- 1.5 equals 384/256
- 384 is stored, 256 is inferred because it is a Q8 number.
If the Q number's base is to be maintained (n remains constant) the Q number math operations must keep the denominator constant. The following formulas show math operations on the general Q numbers and .
Because the denominator is a power of two the multiplication can be implemented as an arithmetic shift to the left and the division as an arithmetic shift to the right; on many processors shifts are faster than multiplication and division.
To maintain accuracy the intermediate multiplication and division results must be double precision and care must be taken in rounding the intermediate result before converting back to the desired Q number.
Using C the operations are (note that here, Q refers to the fractional part's number of bits) :
Addition[edit]
With saturation
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Unlike floating point ±Inf, saturated results are not sticky and will unsaturate on adding a negative value to a positive saturated value (0x7FFF) and vice versa in that implementation shown. In assembly language, the Signed Overflow flag can be used to avoid the typecasts needed for that C implementation.
Subtraction[edit]
Multiplication[edit]
Division[edit]
See also[edit]
References[edit]
- ^'ARM Developer Suite AXD and armsd Debuggers Guide'. 1.2. ARM Limited. 2001 [1999]. Chapter 4.7.9. AXD > AXD Facilities > Data formatting > Q-format. ARM DUI 0066D. Archived from the original on 2017-11-04.
- ^'Chapter 4.7.9. AXD > AXD Facilities > Data formatting > Q-format'. RealView Development Suite AXD and armsd Debuggers Guide(PDF). 3.0. ARM Limited. 2006 [1999]. pp. 4–24. ARM DUI 0066G. Archived(PDF) from the original on 2017-11-04.
Further reading[edit]
Dsp Quattro 5 2 15 Equals In A Fraction
- Oberstar, Erick L. (2007-08-30) [2004]. 'Fixed Point Representation & Fractional Math'(PDF). 1.2. Oberstar Consulting. Archived(PDF) from the original on 2017-11-04. Retrieved 2017-11-04. (Note: the accuracy of the article is in dispute; see discussion.)
External links[edit]
- 'Q-Number-Format Java Implementation'. Archived from the original on 2017-11-04. Retrieved 2017-11-04.
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Q_(number_format)&oldid=966966796'
The following is a list of fifteen competency areas that have been approved by the NADSP Executive Committee. Each Competency area has corresponding skill statements. These skill statements describe the knowledge and skills DSPs must have to demonstrate competency in each area (see below). In deciding on which competency areas to focus, applicants should think about the things they currently do in their everyday work or areas in which they would like to become more knowledgeable and skillful. Through each competency area, DSPs have the opportunities to address challenges, work on issues identified by the person they support or assist a person in looking in a particular goal. For example, an applicant may provide support to a person with a communication challenge. The applicant could use a work sample to demonstrate how they helped the person they support to develop a picture communication board.
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Area 1: Participant Empowerment
The Direct Support Professional enhances the ability of the participant to lead a self-determining life by providing the support and information necessary to build self-esteem, and assertiveness; and to make decisions.
Skill Statements
- The competent DSP assists and supports the participant to develop strategies, make informed choices, follow through on responsibilities, and take risks.
- The competent DSP promotes participant partnership in the design of support services, consulting the person and involving him or her in the support process.
- The competent DSP provides opportunities for the participant to be a self-advocate by increasing awareness of self-advocacy methods and techniques, encouraging and assisting the participant to speak on his or her own behalf, and providing information on peer support and self-advocacy groups.
- The competent DSP provides information about human, legal, civil rights and other resources, facilitates access to such information and assists the participant to use information for self-advocacy and decision making about living, work, and social relationships.
Area 2: Communication
The Direct Support Professional should be knowledgeable about the range of effective communication strategies and skills necessary to establish a collaborative relationship with the participant.
Skill Statements
- The competent DSP uses effective, sensitive communication skills to build rapport and channels of communication by recognizing and adapting to the range of participant communication styles.
- The competent DSP has knowledge of and uses modes of communication that are appropriate to the communication needs of participants.
- The skilled DSP learns and uses terminology appropriately, explaining as necessary to ensure participant understanding.
Area 3: Assessment
The Direct Support Professional should be knowledgeable about formal and informal assessment practices in order to respond to the needs, desires and interests of the participants.
Skill Statements
- The competent DSP initiates or assists in the initiation of an assessment process by gathering information (e.g., participant’s self-assessment and history, prior records, test results, additional evaluation) and informing the participant about what to expect throughout the assessment process.
- The competent DSP conducts or arranges for assessments to determine the needs, preferences, and capabilities of the participants using appropriate assessment tools and strategies, reviewing the process for inconsistencies, and making corrections as necessary.
- The competent DSP discusses findings and recommendations with the participant in a clear and understandable manner, following up on results and reevaluating the findings as necessary
Area 4: Community and Service Networking
The Direct Support Professional should be knowledgeable about the formal and informal supports available in his or her community and skilled in assisting the participant to identify and gain access to such supports.
Skill Statements
- The competent DSP helps to identify the needs of the participant for community supports, working with the participant’s informal support system, and assisting with, or initiating identified community connections.
- The competent DSP researches, develops, and maintains information on community and other resources relevant to the needs of participants.
- The competent DSP ensures participant access to needed and available community resources coordinating supports across agencies.
- The competent DSP participates in outreach to potential participants.
Area 5: Facilitation of Services
The Direct Support Professional is knowledgeable about a range of participatory planning techniques and is skilled in implementing plans in a collaborative and expeditious manner.
Skill Statements
- The competent DSP maintains collaborative professional relationships with the participant and all support team members (including family/friends), follows ethical standards of practice (e.g., confidentiality, informed consent, etc.), and recognizes his or her own personal limitations.
- The competent DSP assists and/or facilitates the development of an individualized plan based on participant preferences, needs, and interests.
- The competent DSP assists and/or facilitates the implementation of an individualized plan to achieve specific outcomes derived from participants’ preferences, needs and interests.
- The competent DSP assists and/or facilitates the review of the achievement of individual participant outcomes.
Area 6: Community Living Skills & Supports
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The Direct Support Professional has the ability to match specific supports and interventions to the unique needs of individual participants and recognizes the importance of friends, family and community relationships.
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- The competent DSP assists the participant to meet his or her physical (e.g., health, grooming, toileting, eating) and personal management needs (e.g., human development, human sexuality), by teaching skills, providing supports, and building on individual strengths and capabilities.
- The competent DSP assists the participant with household management (e.g., meal prep, laundry, cleaning, decorating) and with transportation needs to maximize his or her skills, abilities and independence.
- The competent DSP assists with identifying, securing and using needed equipment (e.g., adaptive equipment) and therapies (e.g., physical, occupational and communication).
- The competent DSP supports the participant in the development of friendships and other relationships.
- The competent community based support worker assists the participant to recruit and train service providers as needed.
Area 7: Education, Training & Self-Development
The Direct Support Professional should be able to identify areas for self improvement, pursue necessary educational/training resources, and share knowledge with others.
Skill Statements
- The competent DSP completes required training education/certification, continues professional development, and keeps abreast of relevant resources and information.
- The competent DSP educates participants, co-workers and community members about issues by providing information and support and facilitating training.
Area 8: Advocacy
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The Direct Support Professional should be knowledgeable about the diverse challenges facing participants (e.g., human rights, legal, administrative and financial) and should be able to identify and use effective advocacy strategies to overcome such challenges.
Skill Statements
- The competent DSP and the participant identify advocacy issues by gathering information, reviewing and analyzing all aspects of the issue.
- The competent DSP has current knowledge of laws, services, and community resources to assist and educate participants to secure needed supports.
- The competent DSP facilitates, assists, and/or represents the participant when there are barriers to his or her service needs and lobbies decision-makers when appropriate to overcome barriers to services.
- The competent DSP interacts with and educates community members and organizations (e.g., employer, landlord, civic organization) when relevant to participant’s needs or services.
Area 9: Vocational, Educational & Career Support
The Direct Support Professional should be knowledgeable about the career and education related concerns of the participant and should be able to mobilize the resources and support necessary to assist the participant to reach his or her goals.
Skill Statements
- The competent DSP explores with the participant his/her vocational interests and aptitudes, assists in preparing for job or school entry, and reviews opportunities for continued career growth.
- The competent DSP assists the participant in identifying job/training opportunities and marketing his/her capabilities and services.
- The competent DSP collaborates with employers and school personnel to support the participant, adapting the environment, and providing job retention supports.
Area 10: Crisis Prevention and Intervention
The Direct Support Professional should be knowledgeable about crisis prevention, intervention and resolution techniques and should match such techniques to particular circumstances and individuals.
Skill Statements
- The competent DSP identifies the crisis, defuses the situation, evaluates and determines an intervention strategy and contacts necessary supports.
- The competent DSP continues to monitor crisis situations, discussing the incident with authorized staff and participant(s), adjusting supports and the environment, and complying with regulations for reporting.
Area 11: Organizational Participation
The Direct Support Professional is familiar with the mission and practices of the support organization and participates in the life of the organization.
Skill Statements
- The competent DSP contributes to program evaluations, and helps to set organizational priorities to ensure quality.
- The competent DSP incorporates sensitivity to cultural, religious, racial, disability, and gender issues into daily practices and interactions.
- The competent DSP provides and accepts co-worker support, participating in supportive supervision, performance evaluation, and contributing to the screening of potential employees.
- The competent DSP provides input into budget priorities, identifying ways to provide services in a more cost-effective manner.
Area 12: Documentation
The Direct Support Professional is aware of the requirements for documentation in his or her organization and is able to manage these requirements efficiently.
Skill Statements
- The competent DSP maintains accurate records, collecting, compiling and evaluating data, and submitting records to appropriate sources in a timely fashion.
- The competent DSP maintains standards of confidentiality and ethical practice.
- The competent DSP learns and remains current with appropriate documentation systems, setting priorities and developing a system to manage documentation.
Area 13: Building and Maintaining Friendships and Relationships
Support the participant in the development of friendships and other relationships.
Skill Statements
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- The competent DSP assists the individual as needed in planning for community activities and events (e.g., making reservation, staff needs, money, materials, accessibility).
- The competent DSP assists the individual as needed in arranging transportation for community events.
- The competent DSP documents community activities and events.
- The competent DSP encourages and assists the individual as needed in facilitating friendships and peer interactions.
- The competent DSP encourages and assists the individual as needed in communication with parents/family (e.g., phone calls, visits, letters).
- The competent DSP implements individual supports regarding community activities.
- The competent DSP provides incentive or motivation for consumer involvement in community outings.
- The competent DSP assists the individual as needed in getting to know and interacting with his/her neighbors.
- The competent DSP encourages and assists the individual as needed in dating.
- The competent DSP encourages and assists the individual as needed in communicating with social workers and financial workers.
Area 14: Provide Person Centered Supports
Skill Statements
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- The competent DSP provides support to people using a person centered approach.
- The competent DSP modifies support programs and interventions to ensure they are person centered.
- The competent DSP challenges co-workers and supervisors to use person centered practices.
- The competent DSP is knowledgeable about person centered planning techniques.
The competent DSP assists individuals in developing person centered plans.
Area 15: Supporting Health and Wellness
Promotes the health and wellness of all consumers.
Skill Statements
- Administers medications accurately and in accordance with agency policy and procedures.
- Observes and implements appropriate actions to promote healthy living and to prevent illness and accidents.
- Uses appropriate first aid/safety procedures when responding to emergencies.
- Assists individuals in scheduling, keeping, and following through on all health appointments.
- Assists individuals in completing personal care (e.g., hygiene and grooming) activities.
- Assists with identifying, securing and using needed adaptive equipment (i.e. adaptive equipment) and therapies (e.g., physical, occupational, speech, respiratory, psychological).
- Assists individuals in implementing health and medical treatments.
- Assists individuals to take an active role in their health care decisions.