Solutions to Sample Exercises for Quiz 1
Number Conversions, Signed Integer Representations, and Binary Addition
How does one decorate a 31-year-old's birthday cake with only five candles?
31 = 111112
Perform the following number system conversions:
11010112 = 10710 F3A516 = 6237310
1740038 = 6349110 AB3D16 = 4383710
101101112 = 18310 71568 = 369410
Perform the following number system conversions:
11010112 = 6B16 1740038 = 1111 1000 0000 00112
101101112 = B716 F3A516 = 1111 0011 1010 01012
110110012 = 3318 AB3D16 = 1010 1011 0011 11012
Perform the following number system conversions:
12510 = 0111 11012 348910 = 66418
20910 = 1101 00012 971410 = 227628
13210 = 1000 01002 2385110 = 5D2B16
5719010 = DF6616 143510 = 26338
6511310 = FE5916
Add the following pairs of binary numbers, showing all carries:
Carries: 1 100010 1 011000 1 11111110 1 1000000
110101 101110 11011101 1110010
+11001 +100101 +1100011 +1101101
------ ------ -------- -------
001110 010011 01000000 1011111
Give the 8-bit signed-magnitude, one's-complement, two's-complement, and
BCD representation for each of the following decimal numbers:
decimal: 18 115 79 -49 -3 -100
sign-mag: 0001 0010 0111 0011 0100 1111 1011 0001 1000 0011 1110 0100
1's-comp: 0001 0010 0111 0011 0100 1111 1100 1110 1111 1100 1001 1011
2's-comp: 0001 0010 0111 0011 0100 1111 1100 1111 1111 1101 1001 1100
BCD: 0001 1000 0111 1001 1101 0011
0001 0001 0101 1101 0100 1001 1101 0001 0000 0000
(assuming '-' is 1101 as per the textbook)
Fill in the ICC (Integer Condition Code) bits for the following 8-bit
two's-complement additions [NZVC bits]:
11010110 10111001 01011101 00100110
+10101001 +11010110 +00100001 +01011010
--------- --------- --------- ---------
01111111 10001111 01111110 10000000
N Z V C N Z V C N Z V C N Z V C
---------- ---------- ---------- ----------
0 0 1 1 1 0 0 1 0 0 0 0 1 0 1 0
What do each of the Condition Code bits mean?
What does it mean if the bit is a 0?
What does it mean if the bit is a 1?
N = Negative bit
0 = result not negative
1 = result is negative
Z = Zero bit
0 = result not equal to the value zero
1 = result is equal to the value zero
V = Overflow bit
0 = operation did not cause an overflow (result valid)
1 = operation did cause an overflow (result not valid)
C = Carry bit
0 = operation did not produce a carry out
1 = operation did produce a carry out
Why do HFC, IBM, and TWA come before Haag, Iacocca, and Taaffe,
respectively, in the phone book?
They are sorted by ordinal values of their ASCII characters. Check the
ASCII character chart. Uppercase characters come before lowercase
characters.