Find the 16-bit 2’s complementary binary representation for decimal number 1987
ID: 3702686 • Letter: F
Question
Find the 16-bit 2’s complementary binary representation for decimal number 1987 and -1987
What are the 16-bit 1’s and 2’s complements of the following binary numbers (i.e. negate the following numbers under 1’s and 2’s complement number systems), 0000000000010000, 1000111100001001, 0100111000100100?
Add the following 12-bit binary 2’s complement numbers. Then convert each number to decimal and check the results, 011001101101+111010111011, 101011001100+111111111100.
Use the format SEEEEMMMMMMM (4 bits exponent and 7 bits mantissa). The exponent is stored excess-6. The implied decimal point is at the beginning of the mantissa. The sign is 1 for a negative number. Answer following questions:
Convert the decimal number 235 to floating point.
What is the range of numbers that can be stored in this format?
If we ask the computer to output the number stored as a. in decimal format, what the display will be?
Explanation / Answer
1) Given Decimal Number 1987- (0000011111000011) in binary
1's Complement means make zeros to ones ,ones to zeros
1's complement of 1987=1111100000111100
2's complement means add 1 to 1's complement .So, 1111100000111101
-1987 equals 2's complement of positive decimal that is 1111100000111101
1's complement for -1987 0000011111000010
2's complement for -1987=0000011111000011
2)
Given binar number-0000000000010000
1's complement-1111111111101111
2's complement-1111111111110000
Given binary number:1000111100001001
1's complement-0111000011110110
2's complement-0111000011110111
Given binary number-0100111000100100
1's complement-1011000111011011
2's complement-1011000111011100
3)Given 2's complement binary numbers -- 011001101101+111010111011= 01010100101000
1645+ 3771 =5416
-- 101011001100+111111111100 = 01101011001000
2764+ 4092 =6856
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