Homework 5

Max marks: 85

Problem 1 Determine the decimal values of the

following unsigned numbers (()b indicates a base

b representation) (25 marks):

1. (0111011110)2

2. (1011100111)2

3. (3751)8

4. (A25F)16

5. (F0F0)16

Problem 2 Determine the decimal values of the

following 1’s complement binary numbers (15

marks):

1. 0111011110

2. 1011100111

3. 1111111110

Problem 3 Determine the decimal values of the

following 2’s complement numbers (15 marks):

1. 0111011110

2. 1011100111

3. 1111111110

Problem 4 Convert the decimal numbers 73,

1906, -95, and -1630 into signed 12-bit numbers

in the following representations (20 marks):

1. Sign and magnitude

2. 1’s complement

3. 2’s complement

Problem 5 Show that the circuit in Figure 1

implements the full-adder specified in Table 1 (10

marks).

ci xi yi ci+1 si

0 0 0 0 0

0 0 1 0 1

0 1 0 0 1

0 1 1 1 0

1 0 0 0 1

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1

Table 1: Truth table for Full adder

Figure 1: A decomposed implementation of the

full-adder circuit.

1