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Number systems
Comprehend the reasons and methods by which computers utilize binary to represent various types of data. Note: All data must be converted to binary for computer processing, which involves logic gates and storage in registers.
6
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60
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42
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90 min
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CambridgeIGCSEComputer ScienceData representation
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Number systems outcomes6 objectives
- Comprehend the reasons and methods by which computers utilize binary to represent various types of data. Note: All data must be converted to binary for computer processing, which involves logic gates and storage in registers.
- (a) Grasp the concepts of denary, binary, and hexadecimal number systems. (b) Be able to convert between (i) positive denary and positive binary, (ii) positive denary and positive hexadecimal, (iii) positive hexadecimal and positive binary. Note: Denary is base 10, binary is base 2, and hexadecimal is base 16. Only integer values will be used, and conversions must be performed in both directions, with a maximum binary number length of 16 bits.
- Recognize the advantages of using hexadecimal for data representation. Note: Identify areas in computer science where hexadecimal is applied, as it provides a more human-readable format compared to binary due to its shorter length.
- (a) Add two positive 8-bit binary numbers. (b) Understand the concept of overflow in binary addition and its causes. Note: An overflow error occurs if the result exceeds 255 in an 8-bit register, which has a defined limit for representation or storage, such as 16 bits.
- Execute a logical binary shift on a positive 8-bit binary number and comprehend its impact on the number. Note: Perform logical left and right shifts, including multiple shifts. Bits shifted out of the register are lost, and zeros are introduced at the opposite end. The integer is multiplied or divided based on the shift direction, resulting in the loss of significant bits.
- Utilize the two’s complement system to represent both positive and negative 8-bit binary integers. Note: Convert positive and negative binary or denary integers to and from two’s complement 8-bit integers.
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