Integers: signed magnitude

Signed magnitude

Reserve one particular bit for the sign.

Sign bit: If msb is 0, then positive value, if msb is 1, then negative value.

Converting base 10 to N-bit signed magnitude (SM):

1. Ignoring sign, convert base 10 value to binary.

2. If less than (N-1) bits, pad rest of bits to (N-1) with 0.

3. If negative, set msb to 1.

Converting N-bit SM to base 10:

1. Convert lower (N-1) bits to base 10.

2. If msb is 1, put minus sign in front of number.

Example:

Convert 3 in base 10 to 4-bit SM:

binary value: 11

using 3 bits: 011

with sign bit: 0011

Convert -3 in base 10 to 4-bit SM:

binary value: 11

using 3 bits: 011

with sign bit: 1011

What about 15?

binary value: 1111

However, this is already 4 bits, and the sign bit needs to be 0 for positive value.