Coen 1

Fall 2000

Homework 2 ANSWERS

1. Decimal

a. 512 + 256 + 64 + 32 + 4 + 1 = 86910
 b. 410
 c. 64 + 32 + 16 + 8 + 4 + 2 + 1 = 12710

Octal

Simply group as sets of 3 binary digits, starting at the right, and write down the equivalent base 8 number

a. 001 101 100 101 = 15458
 b. 100 = 48

c. 001 111 111 = 1778

Hexadecimal

This time group in sets of 4 binary digits. Hexadecimal requires 16 digits, for the equvalents of the decimal values 0 to 15. So use the letters A (10), B (11), C (12), D (13), E (14), F (15).

a. 0011 0110 0101 = 36516
 b. 0100 = 416
 c. 0111 1111 = 7F16

2. a. 25510 = 111111112
 b. 16310 = 101000112
 c. 122010 = 100110001002

3.
a. 111111111112
 +000000000012
 1000000000002

b. 101110011012
 + 011000100102
 1000110111112

c. 013758
 + 514228
 530178

d. 82FA16
 + 912116
 1141B16

4. a. 110010010112
- 000110001112
 101100001002

b. 10000000002
 -00000000012
 1111111112

5. The truth table is given below:

A

B

C

D

B or C

A and (prev col)

(prev col) nand D

0

0

0

0

0

0

1

0

0

0

1

0

0

1

0

0

1

0

1

0

1

0

0

1

1

1

0

1

0

1

0

0

1

0

1

0

1

0

1

1

0

1

0

1

1

0

1

0

1

0

1

1

1

1

0

1

1

0

0

0

0

0

1

1

0

0

1

0

0

1

1

0

1

0

1

1

1

1

0

1

1

1

1

0

1

1

0

0

1

1

1

1

1

0

1

1

1

0

1

1

1

0

1

1

1

1

1

1

1

1

1

0

 

  1. Write the sum-of-products expression for the Cout column of the truth table above.
    1. A’BCin + AB’Cin + ABCin’ + ABCin

     

  2. Draw the circuit equivalent to your answer for problem 6.

C is the carry in