Conference Topic:
Select two decimal numbers between -60 and +60. Convert the numbers into 8 bit unsigned numbers with negative numbers in the 2's complement form. (Remember that positive numbers have the leftmost bit =0 and negative numbers have the leftmost bit =1).
Add the two numbers together to generate an eight-bit binary result. Show your work.
Response:
Theresa L. Ford on 03-19-2004
Calculate 5010 + -4910.
1. Convert Decimals to Binary
1.A. 5010 = ?2
5010 = 010 + 010 + 3210 + 1610 + 010 + 010 + 210 + 010
0 0 1 1 0 0 1 0
5010 = 001100102
OR:
5010 / 210 = 2510 R 010
2510 / 210 = 1210 R 110
1210 / 210 = 610 R 010
610 / 210 = 310 R 010
310 / 210 = 110 R 110
110 / 210 = 010 R 110
Read from end to beginning ( 110010 ).
Pad left with zeros to 8 bits. ( 00110010 ).
5010 = 001100102
1.B. -4910 = ?2 in 2's compliment form
-4910 = -12810 + 6410 + 010 + 010 + 810 + 410 + 210 + 110
1 1 0 0 1 1 1 1
-4910 = 110011112
OR: (Invert and Add 1)
4910 = 010 + 010 + 3210 + 1610 + 010 + 010 + 010 + 110
0 0 1 1 0 0 0 1
4910 = 001100012
Invert = 110011102
Add 1 = 110011112
-4910 = 110011112
2. Add Binary
5010 = 001100102
-4910 = 110011112
001100102
+ 110011112
12 1, no carry
1
001100102
+ 110011112
012 0, carry 1
11
001100102
+ 110011112
0012 0, carry 1
111
001100102
+ 110011112
00012 0, carry 1
1111
001100102
+ 110011112
000012 0, carry 1
11111
001100102
+ 110011112
0000012 0, carry 1
111111
001100102
+ 110011112
00000012 0, carry 1
111111
001100102
+ 110011112
000000012 0, overflow 1
000000012 = 110
010 + 010 + 010 + 010 + 010 + 010 + 010 + 110 = 110
3. Summary
5010 001100102
+ -4910 +110011112
110 000000012