MATH SOLVE

3 months ago

Q:
# Determine the decimal value of each signed binary number in the sign-magnitude form: (a) 10011001 (b) 01110100 (c) 10111111

Accepted Solution

A:

For signed-magnitude numbers, the most significant bit (leftmost) is used for the sign. 1 is negative and 0 is positive. We also read from right to left.

a. 10011001

2^0 + 2^3 + 2^4 = 1 + 8 + 16 = 25, and the final answer should be -25 because there's a 1 on the leftmost.

b. 01110100

2^2 + 2^4 + 2^5 + 2^6 = 4 + 16 + 32 + 64 = 116, and this is the final answer because there's a 0 on the leftmost.

c. 10111111

2^0 + 2^1 + 2^2 + 2^3 + 2^4 + 2^5 = 1 + 2 + 4 + 8 + 16 + 32 = 63, and the final answer is -63 because there'a 1 on the leftmost.

a. 10011001

2^0 + 2^3 + 2^4 = 1 + 8 + 16 = 25, and the final answer should be -25 because there's a 1 on the leftmost.

b. 01110100

2^2 + 2^4 + 2^5 + 2^6 = 4 + 16 + 32 + 64 = 116, and this is the final answer because there's a 0 on the leftmost.

c. 10111111

2^0 + 2^1 + 2^2 + 2^3 + 2^4 + 2^5 = 1 + 2 + 4 + 8 + 16 + 32 = 63, and the final answer is -63 because there'a 1 on the leftmost.