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Questions and Answers
What is the primary usage of hexadecimal numbers in URLs?
What is the primary usage of hexadecimal numbers in URLs?
Signed integers can only have positive values.
Signed integers can only have positive values.
False
What is the formula to calculate the maximum value of an unsigned integer with n bits?
What is the formula to calculate the maximum value of an unsigned integer with n bits?
2n - 1
Whole numbers such as 5, 7, 12, and 3988, are called ______________________.
Whole numbers such as 5, 7, 12, and 3988, are called ______________________.
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Match the following number systems with their characteristics:
Match the following number systems with their characteristics:
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Why are hexadecimal numbers used in assembly code and machine code?
Why are hexadecimal numbers used in assembly code and machine code?
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Unsigned integers have negative values by definition.
Unsigned integers have negative values by definition.
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What is the minimum value that can be represented with n bits?
What is the minimum value that can be represented with n bits?
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The highest value unsigned integer that can be represented with 16 bits is ______________________.
The highest value unsigned integer that can be represented with 16 bits is ______________________.
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What is the base of the decimal number system?
What is the base of the decimal number system?
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Study Notes
Binary Representation
- 78 (decimal) can be represented in binary as 01001110, using the place values 64 + 8 + 4 + 2 = 78.
- A negative number in binary representation has the first (most significant) binary digit as 1, for example, -95 (decimal) can be represented as 10010111, using the place values -128 + 32 + 1 = -95.
Two's Complement Method
- To represent a negative number using two's complement, first take one's complement (invert all the values – 0's to 1 and 1's to 0) for the given binary number.
- Then, add 1 to the result, for example, the binary representation of -35 is 11011101.
Data Storage
- All types of data, including numbers, text, images, and sound, must be held in binary form inside the computer.
- Whole numbers are called integers, and one byte of storage can store all the numbers from 0 to 255.
- When you want to represent the next number, i.e., ten, you use a combination of these digits, i.e., 10.
Binary System
- Binary is a base two system, with only two different digits: 0 and 1.
- Binary starts off in the same way as a decimal: 0 (zero), 1 (one), using a combination of 0's and 1's to represent different values.
- The columns in binary represent successive powers of two, just like the columns in decimal represent different powers of ten.
Binary Conversion
- A decimal number can be expressed in binary form using a large number of digits, for example, the number 65 can be expressed in binary form as 1000001.
- These binary codes can be represented using hexadecimal values or decimal values.
Hexadecimal Representation
- Hexadecimal numbers are used in assembly code and machine code, as they are easier, faster, and less error-prone to write code compared to binary.
- Hexadecimal numbers can be used to represent URLs or web addresses, for example, www.hodder.co.uk becomes %77%77%77%2E%68%6F%64%64%65%72%2E%63%6F%2E%75%6B.
Binary Integers
- Whole numbers such as 5, 7, 12, and 3988 are called integers.
- Unsigned integers have positive values by definition, while signed integers can be positive or negative.
- Unsigned integers in binary are represented as 2^n, where n is the number of bits.
- The minimum value that can be represented with n bits is 0, and the maximum value is 2^n-1.
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Description
This quiz covers the representation of decimal numbers in binary format, including positive and negative numbers, using place values and two's complement method.
