Question

1. (8%) For a 8-bit sequence is 1101 0111. What is its content if it represents (a) two decimal digits in BCD? (b) two decimal number in the Excess-3 code? (c) an 8-bit unsigned number? (d) an 8-bit signed number?

Answer 1

a)

The BCD equivalent of 1101 = 0011

The BCD equivalent of 0111 = 0111

Hence, the equivalent decimal digits are:

37

b)

1101 + 0011 = 10000 = 16₁₀

0111 + 0011 = 1010 = 10₁₀

Hence, the equivalent decimal numbers are:

16 10

c)

= 1 * 2⁷ + 1 * 2⁶ + 0 * 2⁵ + 1 * 2⁴ + 0 * 2³ + 1 * 2² + 1 * 2¹ + 1 * 2⁰

= 128 + 64 + 16 + 4 + 2 + 1

= 215₁₀

d)

Here, the first bit (Most significant bit) is 1, this means that the number is negative.

Magnitude = 1010111₂

= 1 * 2⁶ + 0 * 2⁵ + 1 * 2⁴ + 0 * 2³ + 1 * 2² + 1 * 2¹ + 1 * 2⁰

= 64 + 16 + 4 + 2 + 1

= 87₁₀

Hence, the equivalent signed decimal number = -87