Number systems

What the syllabus asks of you

• Understand how and why computers use • Any form of data needs to be converted to binary to represent all forms of data binary to be processed by a computer • Data is processed using logic gates and stored in registers
• (a) Understand the denary, binary and • Denary is a base 10 system hexadecimal number systems • Binary is a base 2 system • Hexadecimal is a base 16 system (b) Convert between • Values used will be integers only (i) positive denary and positive binary • Conversions in both directions, e.g. denary to (ii) positive denary and positive binary or binary to denary hexadecimal • Maximum binary number length of 16-bit (iii) positive hexadecimal and positive binary
• Understand how and why hexadecimal is used • Areas within computer science that as a beneficial method of data representation hexadecimal is used should be identified • Hexadecimal is easier for humans to understand than binary, as it is a shorter representation of binary
• (a) Add two positive 8-bit binary integers (b) Understand the concept of overflow and • An overflow error will occur if the value is why it occurs in binary addition greater than 255 in an 8-bit register • A computer or a device has a predefined limit that it can represent or store, for example 16-bit • An overflow error occurs when a value outside this limit should be returned Candidates should be able to: Notes and guidance
• Perform a logical binary shift on a positive 8-bit • Perform logical left shifts binary integer and understand the effect this • Perform logical right shifts has on the positive binary integer • Perform multiple shifts • Bits shifted from the end of the register are lost and zeros are shifted in at the opposite end of the register • The positive binary integer is multiplied or divided according to the shift performed • The most significant bit(s) or least significant bit(s) are lost
• Use the two’s complement number system to • Convert a positive binary or denary integer to a represent positive and negative 8-bit binary two’s complement 8-bit integer and vice versa integers • Convert a negative binary or denary integer to a two’s complement 8-bit integer and vice versa