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How many bits does it take to represent a piece of data that could have one of 1000 values?
10 bits (each has a possible value of 0 or 1, 2^10 = 1024, but 2^9 only = 512).
What is two's complement notation? What types of calculations does it allow?
Two's complement notation is a way of representing both positive and negative numbers in binary. It prevents overflow.
When adding two binary numbers, if the first digits are the same is there a chance of overflow?
Yes, because a binary number that starts with a 1 is negative, but a binary number that starts with 0 is positive. If they both start with the same digit, they are both on the same side of zero.
When adding two binary numbers that start with the same digits, how can you tell if overflow has occurred?
Overflow has occurred if the first digit of the result is not the same as the first digit of the two numbers being added.
What do all even binary numbers end in?
What do all odd binary numbers end in?
Describe how to convert -44 in base 10 to binary using Two's complement.
- First, convert 44 to binary by determining how many 128s, 64s, 32s, 16s, 8s, 4s, 2s, and 1s are in it.
- Then, working from the right, underline all of the zeros that you pass until you get to a 1. Underline the 1 also.
- Now, working from the left, flip the digits UNTIL you get to the underlined digits. Just "bring down" the underlined digits.
- e.g. - 44 in binary is 1-32, 1-8, and 1-4. This is 00101100. This becomes 11010100.
Convert the number 10110100 to decimal.
- Note that this number starts with a 1, therefore it is negative.
- Working from the right, flip the digits until you get to the last 1. Starting with that 1, just "bring down" the rest of the digits.
- Now, determine how many 128s, 64s, 32s, 16s, 8s, 4s, 2s, and 1s are in it.
- Compute the sum.
- IMPORTANT: Make the answer negative.
Make a binary to hexadecimal conversion chart.
- 0 0000
- 1 0001
- 2 0010
- 3 0011
- 4 0100
- 5 0101
- 6 0110
- 7 0111
- 8 1000
- 9 1001
- A 1010
- B 1011
- C 1100
- D 1101
- E 1110
- F 1111
What is a radix?
It is the name for the symbol used to separate whole numbers from partial numbers. For example, in base-10 it is called a decimal point.
How is a real number stored in floating-point notation?
- It is assumed that the first digit is always a 1, so it is not stored.
- There are 32 bits allocated to a floating point number:
- the first bit is a sign bit (0 for positive, 1 for negative)
- the next eight bits are a bias-127 exponent (127 plus the actual exponent)
- the last 23 bits are the mantissa (the exponent-less scientific notation value, without the leading 1)
What is ASCII?
- ASCII - American Standard Code for Information Interchange - was developed as a means of converting text into a binary notation.
- Each character has a 7-bit binary representation.
What is the Unicode character set?
It is an character set that was designed for international use. Each character uses 16 bits, allowing many more characters. The first 256 characters in unicode correspond exactly to ASCII.
How do fax machines transmit data over telephone lines?
- They convert each document into a grid of tiny black and white triangles. The data is compressed by using the length and color of each rectangle (long rectangles don't require as much data proportionally as shorter rectangles).
- The name of the code used is CCITT Fax Conversion Code.