Computer Architecture
Tutorial 3 – Number Representation and Binary Arithmetic
1) Convert the following binary numbers to decimal:
(a) 0110, (b) 1011, (c) 10101010
2) Convert the following binary numbers to hexadecimal:
(a) 1110, (b) 11011, (c) 1010111101110010
3) Convert the following decimal numbers to binary and hexadecimal:
(a) 12, (b) 27, (c) 96
4) For an 8-bit group, work out the representation for -3710 in
a) Sign & Magnitude
b) One’s Complement
c) Two’s Complement
d) Excess-255 (Note: The n in Excess-n does not have to equal 2
m
– 1, where m is
the number of bits in the bit-group)
e) Excess-128
5) Express 9876510 in Binary Coded Decimal
6) Form the negative equivalent of the following 8-bit Two’s Complement numbers
(a) 00011001, (b) 00011110, (c) 01101000, (d) 01110100
by comparing the resulting bit-patterns to the originals, can you spot a “short cut”
method for the conversion?
7) Perform the following 12-bit two’s complement subtraction
1010 1010 1011
−1011 0000 1101
8) Perform the binary multiplication 10011 x 1101
9) Divide the binary number 1011111 by 101
For questions 7 – 9, check the answer by conversion to decimal