Please explain clearly how to do these problems please. Im getting really stress
ID: 3620004 • Letter: P
Question
Please explain clearly how to do these problems please. Im getting really stressed..Thanks and hope you can help ^_^
a)Consider an 8-bit binary system. Give the 8-bit binary representation for the
complement of the following numbers.
i) 0110 0101 ii) 1010 0001 iii) 1110 0011
[For part a I think i only have to free all the bits and then add 1 right?]
b) Suppose the bit strings in a) representing unsigned binary numbers. Convert the
numbers and their complement to decimal numbers.
c) Suppose the bit strings in a) representing two’s complement numbers. Convert
the numbers and their complement to decimal numbers.
d) Suppose the bit strings in a) representing signed magnitude numbers. Convert
the numbers and their complement to decimal numbers
Explanation / Answer
please rate - thanks a) complement of the number is the bits flipped (0 becomes 1, 1 becomes 0)i) 1001 1010 ii) 0101 1110 iii) 0001 1100 however I think you mean the 2's complement which is the digits flipped +1
i) 1001 1010 + 1
1001 1011 = 2's complement of 0110 0101
ii) 0101 1110 + 1
0101 1110 0101 1111 = 2's complement of 1010 0001
iii) 0001 1100
+ 1
0001 1101 = 2's complement of 1110 0011
b) Suppose the bit strings in a) representing unsigned binary numbers. Convert the
numbers and their complement to decimal numbers.
assign the columns values 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0 and add the column values that have a 1 in them
i) 0110 0101 64+32+4+1=101
2's complement
1001 1011 128+16+8+2+1 = 155
ii) 1010 0001 128+32+1 = 161 2's complement 0101 1111 64+16+8+4+2+1 = 95
iii) 1110 0011
128+64+32+2+1 = 225 2's complement 0001 1101
16+8+4+1 = 29
c) Suppose the bit strings in a) representing two’s complement numbers. Convert
the numbers and their complement to decimal numbers.
i) 0110 0101
sign bit is 0 so positive so just convert 64+32+4+1 = 101
ii) 1010 0001 starts with 1 so negative convert it's 2's complement and add - sign 0101 1110 + 1
0101 1111 =64+16+8+4+2+1 =106 so the number is -106
iii) 1110 0011 again starts with 1 so negative. find 2's complement 0001 1100 + 1
0001 1100 = 16+8+4 = 28 so the number is -28
d) Suppose the bit strings in a) representing signed magnitude numbers. Convert
the numbers and their complement to decimal numbers i) 0110 0101 starts with 0 so positive number 64+32+4+1 =101
ii) 1010 0001 starts with 1 so negative 010 0001 =32+1 = 33 but negative so -33
iii) 1110 0011 starts with 1 so negative 110 0011 =64+32+3+1=100 but negative so -100 if you have any questions message me
b) Suppose the bit strings in a) representing unsigned binary numbers. Convert the
numbers and their complement to decimal numbers.
assign the columns values 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0 and add the column values that have a 1 in them
i) 0110 0101 64+32+4+1=101
2's complement
1001 1011 128+16+8+2+1 = 155
ii) 1010 0001 128+32+1 = 161 2's complement 0101 1111 64+16+8+4+2+1 = 95
iii) 1110 0011
128+64+32+2+1 = 225 2's complement 0001 1101
16+8+4+1 = 29
c) Suppose the bit strings in a) representing two’s complement numbers. Convert
the numbers and their complement to decimal numbers.
i) 0110 0101
sign bit is 0 so positive so just convert 64+32+4+1 = 101
ii) 1010 0001 starts with 1 so negative convert it's 2's complement and add - sign 0101 1110 + 1
0101 1111 =64+16+8+4+2+1 =106 so the number is -106
iii) 1110 0011 again starts with 1 so negative. find 2's complement 0001 1100 + 1
0001 1100 = 16+8+4 = 28 so the number is -28
d) Suppose the bit strings in a) representing signed magnitude numbers. Convert
the numbers and their complement to decimal numbers i) 0110 0101 starts with 0 so positive number 64+32+4+1 =101
ii) 1010 0001 starts with 1 so negative 010 0001 =32+1 = 33 but negative so -33
iii) 1110 0011 starts with 1 so negative 110 0011 =64+32+3+1=100 but negative so -100 if you have any questions message me
b) Suppose the bit strings in a) representing unsigned binary numbers. Convert the
numbers and their complement to decimal numbers.
assign the columns values 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0 and add the column values that have a 1 in them
i) 0110 0101 64+32+4+1=101
2's complement
1001 1011 128+16+8+2+1 = 155
1001 1011 128+16+8+2+1 = 155
ii) 1010 0001 128+32+1 = 161 2's complement 0101 1111 64+16+8+4+2+1 = 95
iii) 1110 0011
128+64+32+2+1 = 225 2's complement 0001 1101
16+8+4+1 = 29
c) Suppose the bit strings in a) representing two’s complement numbers. Convert
the numbers and their complement to decimal numbers.
i) 0110 0101
sign bit is 0 so positive so just convert 64+32+4+1 = 101
ii) 1010 0001 starts with 1 so negative convert it's 2's complement and add - sign 0101 1110 + 1
0101 1111 =64+16+8+4+2+1 =106 so the number is -106
iii) 1110 0011 again starts with 1 so negative. find 2's complement 0001 1100 + 1
0001 1100 = 16+8+4 = 28 so the number is -28
i) 0110 0101
sign bit is 0 so positive so just convert 64+32+4+1 = 101
ii) 1010 0001 starts with 1 so negative convert it's 2's complement and add - sign 0101 1110 + 1
0101 1111 =64+16+8+4+2+1 =106 so the number is -106
iii) 1110 0011 again starts with 1 so negative. find 2's complement 0001 1100 + 1
d) Suppose the bit strings in a) representing signed magnitude numbers. Convert
the numbers and their complement to decimal numbers i) 0110 0101 starts with 0 so positive number 64+32+4+1 =101
ii) 1010 0001 starts with 1 so negative 010 0001 =32+1 = 33 but negative so -33
iii) 1110 0011 starts with 1 so negative 110 0011 =64+32+3+1=100 but negative so -100 if you have any questions message me