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Flashcards Edexcel GCSE Computer Science

2.1 Binary

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What number system do computers primarily use?
Binary
How many base numbers does the binary number system use?
2
What is the base number of the hexadecimal system?
16
What does each digit in a hexadecimal number represent?
4 bits of a binary number
What are the digits used in the hexadecimal system?
0-9 and A-F
Which method is used to represent negative numbers in binary by flipping the bits of the positive value?
One's Complement
In binary, how is the value affected by each place the digits move to the left?
Doubles
What happens to the binary value when it is shifted to the right?
Halves
What is the maximum range of an 8-bit binary number using two's complement?
-127 to 127
What is the primary difference between one's complement and two's complement in binary?
Two's complement adds 1 to the one's complement
In two's complement, how is a negative number represented?
Inverting all bits and adding 1
What is the main advantage of using two's complement over one's complement?
Simplifies the hardware for arithmetic operations
How does the sign and magnitude representation indicate a negative number in binary?
The leftmost bit is set to 1
What is a unique feature of one's complement representation?
It has two representations for zero
What is the first step in converting a binary number to denary?
Identify the value of each binary digit
What does each digit in a binary number represent?
A power of 2
In binary to denary conversion, what happens when you move from right to left across the binary number?
The value of each digit doubles
Convert the 4-bit binary number 1101 to denary.
13
What is the denary equivalent of the 4-bit binary number 0100?
4
If a 4-bit binary number is 1001, what is its denary value?
9
What is the denary value of the 4-bit binary number 0111?
7
Convert the 8-bit binary number 11001001 to denary.
201
What is the denary equivalent of the 8-bit binary number 00011011?
27
If you have an 8-bit binary number 10101010, what is its denary representation?
170
In the denary to binary conversion, what does each '1' or '0' represent?
Whether a specific power of 2 is present or absent
Convert the denary number 6 to a 4-bit binary number.
0110
What is the 4-bit binary equivalent of the denary number 9?
1001
What is its 4-bit binary representation of the number 12?
1100
What is the 4-bit binary equivalent of the denary number 10?
1010
Convert the denary number 15 to an 8-bit binary number.
00001111
Convert the denary number 128 to an 8-bit binary number.
10000000
What is the 8-bit binary equivalent of the denary number 27?
00011011
If you have a denary number 200, what is its 8-bit binary representation?
11001000
Convert the denary number 255 to an 8-bit binary number.
11111111
How many bits are used to represent a single hexadecimal digit in binary?
4 bits
Which hexadecimal digit corresponds to the binary number 1111?
F
What is the binary equivalent of the hexadecimal digit 'A'?
1010
Convert the hexadecimal digit '7' to binary.
0111
What is the binary equivalent of the hexadecimal digit '4'?
100
If a hexadecimal digit is 'B', what is its 4-bit binary representation?
1011
Convert the hexadecimal number '3F' to binary.
00111111
What is the binary equivalent of the hexadecimal number 'A4'?
10100100
If you have a hexadecimal number 'E2', what is its binary representation?
11100010
Convert the hexadecimal number '1C' to binary.
00011100
What base number system is hexadecimal?
Base-16
How many binary bits correspond to one hexadecimal digit?
4 bits
Which digits are used in the hexadecimal system?
0-9 and A-F
Convert the 4-bit binary number 1010 to hexadecimal.
A
What is the hexadecimal equivalent of the 4-bit binary number 0101?
5
If the 4-bit binary number is 1111, what is its hexadecimal value?
F
Convert the 8-bit binary number 11001100 to hexadecimal.
CC
What is the hexadecimal equivalent of the 8-bit binary number 10101010?
AA
If you have an 8-bit binary number 01101001, what is its hexadecimal representation?
69
Convert the 8-bit binary number 10011011 to hexadecimal.
9B
Convert the denary number 15 to hexadecimal.
F
What is the hexadecimal equivalent of the denary number 10?
A
Convert the denary number 255 to hexadecimal.
FF
What is the hexadecimal representation of the denary number 128?
80
Convert the denary number 32 to hexadecimal.
20
Convert the hexadecimal number 'A' to denary.
10
What is the denary equivalent of the hexadecimal number '1F'?
31
Convert the hexadecimal number 'FF' to denary.
255
What is the denary representation of the hexadecimal number '7A'?
122
Convert the hexadecimal number 'C' to denary.
12
What is the result of adding two '1' digits in binary addition?
0 (carry the 1)
In binary addition, what does 'carrying the 1' mean?
Transferring a 1 to the next left column
What is the fundamental rule for adding '0' and '1' in binary?
0 + 1 = 1
What is the result of adding '1 and '1' and '1' in binary
1 (carry the 1)
Add the binary numbers 1 and 0.
1
What is the sum of 1 and 1 in binary?
10
Add the 4-bit binary numbers 0101 and 0011.
1000
What is the result of adding 4-bit binary numbers 1100 and 1001?
10101
Compute the sum of 4-bit binary numbers 1111 and 0001.
10000
Add the 8-bit binary numbers 11001001 and 00111001.
100000010
What is the sum of 8-bit binary numbers 10101010 and 01010101?
11111111
What is an 'overflow' in binary addition?
When the sum exceeds the capacity of the number of bits used, requiring an additional bit
Add the 8-bit binary numbers 11110000 and 01110000 and identify if there's an overflow.
11100000
What does an unsigned binary number represent?
A non-negative integer
What is the key characteristic of one's complement representation of negative numbers?
Inverting all bits of the positive number
How does two's complement representation differ from one's complement?
By adding 1 to the one's complement of the number
What is a limitation of using sign magnitude for representing binary numbers?
It has two representations for zero
Convert the unsigned binary number 01010101 to one's complement
10101010
Convert the unsigned binary number 01101000 to one's complement
10010111
Convert the unsigned binary number 10011011 to two's complement
01100101
Convert the unsigned binary number 00001111 to one's complement
11110000
Convert the unsigned binary number 11110000 to two's complement
00001000
Convert the unsigned binary number 10101010 to one's complement
01010101
Convert the unsigned binary number 00110011 to two's complement
11001101
Convert the unsigned binary number 00000001 to one's complement
11111110
Convert the unsigned binary number 11111111 to two's complement
00000001
Convert the unsigned binary number 01010100 to one's complement
10101011
What is the 4-bit one's complement binary equivalent of the denary number -3?
1100
Convert the denary number -7 to a 4-bit one's complement binary number
1000
Convert the denary number -10 to an 8-bit one's complement binary number
11110101
What is the 8-bit one's complement binary equivalent of the denary number -20?
11101101
Convert the denary number -50 to an 8-bit one's complement binary number
11001101
What is the 4-bit two's complement binary equivalent of the denary number -8?
1000
Convert the denary number -1 to a 4-bit two's complement binary number
1111
Convert the denary number -5 to an 8-bit two's complement binary number
11111011
What is the 8-bit two's complement binary equivalent of the denary number -15?
11110001
Convert the denary number -128 to an 8-bit two's complement binary number
10000000
What is the primary effect of a left binary shift on a number's value?
Doubles the value
What happens to a number's value when a right binary shift is applied?
Halves the value
What is 'overflow' in the context of binary shifts?
When a bit shifts beyond the size of the number representation
In an 8-bit binary number, what happens when a left shift causes the most significant bit to fall off?
Overflow occurs
What is the effect of two consecutive left shifts on a binary number?
The value is quadrupled
Perform a left shift on the binary number 01101010
11010100
Perform a right shift on the binary number 10110011
01011001
What is the result of two left shifts on the binary number 00110001?
11000100
Perform a right shift on the binary number 00010110
00001011
What is the result of performing three left shifts on the binary number 10010001?
10001000
After a right shift, what is the new value of the binary number 01101100?
00110110
Perform two right shifts on the binary number 11001100
00110011
What is the binary number 01010101 after one left shift?
10101010
Perform three right shifts on the binary number 11100000
00011100
What is the result of one left shift on the binary number 00110111?
01101110