Homework 5 binary numbers

Description

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