Extend Number Log For Free

Sign extension is used for signed loads of bytes (8 bits using the lb instruction) and halfwords (16 bits using the lh instruction). Sign extension replicates the most significant bit loaded into the remaining bits.

To sign extend a value from some number of bits to a greater number of bits is easy, just copy the sign bit into all the additional bits in the new format. For example, to sign extend an eight bit number to a 16 bit number, simply copy bit seven of the eight bit number into bits 8.. 15 of the 16 bit number.

We can, of course, use the closed-form formula for sum of geometric series and get the same result. Since the difference is zero, we conclude that sign extension preserves both the sign and the value for two's complement numbers.

Recall: to increase the number of bits in a representation of an integer in two's complement, add copies of the leftmost bit (the sign bit) to the left until you have the desired number of bits. This is called sign extension.

Sign-extending means copying the sign bit of the unextended value to all bits on the left side of the larger-size value.

Recall: to increase the number of bits in a representation of an integer in two's complement, add copies of the leftmost bit (the sign bit) to the left until you have the desired number of bits. This is called sign extension.

Recall: to increase the number of bits in a representation of an integer in two's complement, add copies of the leftmost bit (the sign bit) to the left until you have the desired number of bits. This is called sign extension.

Sign extension is required when you need to add numbers that come from different sized sources. As an example, when you have a signed 8 bit value and need to add it to a signed 32 bit value, the 8 bit value needs to be extended to 32 bit value.

The length of a binary number is given by the value of n, actually it's n+1. For example, a binary number like 101 has a length of 3, something larger, like 10011110 has a length of 8.

A similar concept is zero extension (abbreviated as zext). In a move or convert operation, zero extension refers to setting the high bits of the destination to zero, rather than setting them to a copy of the most significant bit of the source.